A dynamite blast blows a heavy rock straight up with a launch velocityof 160 ft/sec (about 109 mph) . It reaches a height of s = 160t - 16t2 ftafter t sec. When does the rock hit the ground again?

Q: A lamp post 3 m high is 6m from the wall. A man 2 m tall is walking directly from the post toward…

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Q: hot air ballon is hovering 110 meters above the ground and begins to assend at a rate of 17 meters…

A: This is a question of application of differentiation and integration... We will proceed as follows

Q: A5 feet 6 inches tall man is walking away from a lamppost at a rate of 2 ft/sec. If the lamppost is…

A: We have, A 5 feet 6 inches (5.5 feet) tall man is walking away from the lamppost of height 12 feet…

Q: 17 foot ladder is leaning against a wall. If the top slips down the wall at a rate of 3 ft/s, how…

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Q: velocity

A: We have : h=12t2+12t We have to find the velocity of the balloon at the end of the 39 sec.

Q: A cyclist coasts up a 11.3° slope, traveling 19.0 m along the road to the top of the hill. If the…

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Q: Assume the accleration of the object is a(t) = −32 feet per second per second. (Neglect air…

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Q: 16 foot ladder is leaning against a wall. If the top of the ladder slides down the wall at a rate of…

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Q: Find the velocity v of an ocean freighter that is traveling 30° south of east at 30 km/hr.

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Q: A golfer takes a swing from a hill twenty feet above the cup with an initial upwards velocity of 32…

A: It is given that, initial upward velocity from the hill is, v=32 feet per second, angle of swing…

Q: Fireworks are fired up from a platform 3 ft. above the ground with an initial velocity of 125 ft/s.…

A: Given that: Fireworks are fired up from a platform 3 ft. above the ground with an initial velocity…

Q: 3

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Q: A stone is dropped from the edge of a roof, and hits the ground with a velocity of -120 feet per…

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Q: Assuming there is no sag in the string, find the rate at which the kite is moving when 125

A: Considering a right triangle with the data given, the hypotenuse 'c' is 125 feet, base 'b' and the…

Q: A rocket can rise to a height of h(t) = + 0.6t2 feet in t seconds. Find its velocity and…

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Q: A 60-kg skydiver jumps out of an airplane. What is her terminal velocity, in meters per second,…

A: Given, Mass (m) of the skydiver = 60-kg, and k = 10-kg/s

Q: What is the velocity (in ft/s) of a sandbag 0.25 s after it is released from a hot-air balloon that…

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Q: A coin of mass 0.05kg is dropped from the top of the Eiffel tower, which is 300m tall. It…

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Q: Water flows from the bottom of a storage tank at a rate of r(t)=350– 5t litres per minute, where…

A: Given that the water flow from the bottom of a storage tank at a rate, rt=350-5t,  0≤t≤80

Q: A car is slowing down at the rate 0.8 ft/sec². How far will the car move before it stops if its…

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Q: An object is dropped from a 64-foot tower and reaches the ground in 2 seconds. What would the…

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Q: A kite, at a height of 80 feet, is moving horizontally at a rate of 6 feet per second away from the…

A: The height of the kite is, y = 80 ft The rate at which the kite is moving horizontally, dxdt = 6 fts…

Q: A passenger is traveling on a luxury train that is moving west at 80 mph (miles per hour). While…

A: A passenger is travelling on a luxury train that is moving west at 80mph . While running the…

Q: A car is moving at 88 - on a straight road when the driver hits the brakes and begins decelerating…

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Q: A 45-caliber bullet shot straight up from thesurface of the moon would reach a height of s = 832t -…

A: Given, A 45-caliber bullet shot straight up from the surface of the moon would reach a height of…

Q: A spherical snowball melts at a rate of 2 cubic centimeters per hour. How fast is the radius…

A: We know that the volume of a spherical snowball is v = 43πr3 where v is the volume and r is the…

Q: A particle moves along a straight line with a velocity v(t) = t²e²t meters per second after t…

A: A particle moves along a straight line with a velocity v(t)=t2e2t meters per second after t seconds.

Q: A projectile is shot upwards from the surface of the earth with an initial velocity of 120 meters…

A: To determine: The velocity of a projectile after 6 seconds and after 9 seconds where a projectile is…

Q: Jessi launched a toy rocket vertically upward having an initial velocity of 100 feet per second then…

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Q: If a rock is thrown vertically upward from the surface of Mars with velocity 80m/s, its height after…

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Q: A 5-kg bucket is lifted from the ground into the air by pulling in 20 m of rope at a constant speed…

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Q: A car is moving at 60 mi/hr (88 ft/sec) on a straight road when the driver steps on the brake pedal…

A: Given  Initial speed of the car =60 mi/hr (88 ft/sec) deceleration =12 ft/sec^2  time =3 sec

Q: The velocity of a moving object is V (t)=2t +/t in meters per second. What is its displacement, in…

A: We have to find displacement

Q: A car is moving at 60 mi/hr (88 ft/s) on a straight road when thedriver steps on the brake pedal and…

A: Given: u=88 feetsec, a=-10 fts2, t=3 seconds we know that s=ut+12at2…

Q: On Earth, you can easily shoot a paperclip 64 ft straight up into the air with a rubber band. In t…

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Q: A steel ball of mass 4 kg is dropped from a building. If the air resistance is equal to 0.371v, what…

A: Mass of ball m=4 kg Air Resistance =0.371v Now, the formula to find  velocity of ball at time t is:…

Q: .A ball is thrown upward from a height of 15 feet with an initial upward velocity of 5 ft/sec. Use…

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Q: What constant acceleration is required to increase the speedof a car from 30 mih to 50 mih in 5 s?

A: Given: u=30 mihour, v=50 mihour, t=5 second for finding acceleration, first we convert given…

Q: What is the velocity (in ft/s) of a sandbag 3.0 s after it is released from a hot-air balloon that…

A: According to Questions  Initial velocity (u)=0 ft/s  time=t=3s

Q: on the moon, the acceleration of a free falling object is a(t) = -1.6 meters per second per second.…

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Q: A car is traveling at  100km/h when the driver sees an accident80 m ahead and slams on the brakes.…

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Q: After a ball bounces off from the top of a hill, its velocity at t seconds is v(t)=45-30t feet per…

A: Given velocityv(t) = 45 - 30t

Q: Had Galileo dropped a cannonballfrom the Tower of Pisa, 179 ft above the ground, theball’s height…

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Q: Find the acceleration of the potato at 0.5 s ft/s?

A: s(t)=-81t2+225t+3acceleration a(t)=s''(t)consider s(t)=-81t2+225t+3Differentiate with respect to…

Q: Assume gravity is 32 ft/s^2 and no external forces (ex: wind resistance). If you Jump off a 30 ft…

A: The equation for kinematics is- h=ut+12gt2 where, h is height of building (total displacement…

Q: A ball is thrown straight down from the top of a 370-foot building with an initial velocity of -18…

A: Given

Q: ng the shore and 60 meters from the sh mps into the water and swims from the second and swim at a…

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Q: A baseball thrown directly upward at 160 ft/sec has velocity v(t) = 160- 32t ft/sec at time t…

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