A projectile is launched straight upward from Earth's surface at the North Pole. For Earth's radius at the North Pole, use  RE, NP = 6.36 ✕ 106 m. Ignoring air resistance, find the maximum altitude of the projectile above Earth's surface if the launch speed is  2.25 ✕ 103 m/s.

Q: Given an airplane in flight at a cruising speed of 250 m/s, what is the minimum turning radius (in…

A: Speed of the airplane (v)=250 m/s Healthy humans have been shown to detect accelerations as low as…

Q: A secret agent skis off a slope inclined at θ = 29 degrees below horizontal at a speed of v0 = 19.5…

A: Given: slope θ = 29o. speed of an agent vo = 19.5 m/s height h = 18.8 m

Q: A Ferris wheel with a radius of 8.0m makes 1 revolution every 10 s. When he is at the top,…

A:

Q: A particle moves in the xy plane in a circle centered on the origin. At a certain instant the…

A: Given,   At some instant                  Velocity V→ = 7j m/sAcceleration a→ = -3.0 i^ - 2.0 j^…

Q: An object traveling on a circular path at a constant speed of 3.7 m/s is experiencing a centripetal…

A: SOlution: given that v = 3.7 m/s a = 5.2 m/s

Q: If a projectile is thrown from the top of a 20.0 m building at a speed of 25.0 m/sec, at which angle…

A:

Q: Olympus Mons on Mars is the largest volcano in the solar system, at a height of 25 km and with a…

A: Using kinematic equation of motion,

Q: A tracking radar lies in the vertical plane of the path of a rocket which is coasting in unpowered…

A: Given :       θ = 30°   The tracking data :             r = 25×104 ft             r˙ = 4000 ft/sec…

Q: An airplane releases a ball as it flies parallel to the ground at a height of h= 285 m as shown in…

A: We will treat this problem as projectile motion, where a ball is launched with velocity v…

Q: For an object undergoing a uniform circular motion with radius 5.7 m and period 4.35 sec, the…

A:

Q: A secret agent skis off a slope inclined at θ = 28.3 degrees below horizontal at a speed of v0 =…

A:

Q: A projectile is launched horizontally from the top edge of a 20m tall building with a vxo of 25m/s.…

A:

Q: A cannonball is located at the top of a 48.2 m building is shot horizontally with velocity of 112.1…

A:

Q: James Bond is chasing a runaway villain across the tops of several buildings. In order to make it…

A:

Q: At what altitude must a military plane flying horizontally at 175 m/s be in order to deliver relief…

A: Given that, Speed = 175 m/s Distance = 1750 m

Q: An Archer shoots at a target that is 29 km away, and 12.5 m above the ground. If the arrow is…

A:

Q: A football player releases a ball with the initial conditions shown in the figure. Determine the…

A:

Q: "In the circular motion, always the centripetal acceleration is perpendicular to the velocity" O…

A: We need to state whether the given statement is True or False.

Q: A particle moves in a circular path of radius R = 2 m. At some instant of time, its total…

A:

Q: During a portion of a vertical loop, an airplane flies in an arc of radius p = 581 m with a constant…

A: The radial and angular velocity of the plane be calculated as,

Q: A cannon is fired from the ground level, in a flat terrain, making an angle of 30° upwards with the…

A: given,

Q: A projectile is shot toward a hill that is d = 339 m away. The launch angle is e = 58.6 degrees…

A: Ans:- Image-1

Q: H 30° 20m A cannonball is fired from a castle with the trajectory as shown in the figure. The…

A: Given  Vertical velocityu=66 msHorizontal velocityux=180 ms

Q: In a circular motion, if an object has a speed of 34.8m/s, and radius of the circular path is 80.2…

A:

Q: A particle is in uniform circular motion about the origin of an xy coordinate system, moving…

A: The velocity of the particle is,

Q: A particle moves in a circular path of radius R= 2 m. At some instant of time, its total…

A:

Q: A daredevil is attempting to jump his motorcycle over a line of buses parked end to end by driving…

A:

Q: An airplane releases a ball as it flies parallel to the ground at a height of h = 235 m as shown in…

A: Here we are going to solve the value of velocity by using two particular directions i.e. X and Y.

Q: A billiard ball rolls down an inclined plane with length I = 3 m which makes an angle 0 = 30.0 °…

A:

Q: If the height of the water slide is h = 3.8m, and the person's initial speed at the top is 0.70m/s ,…

A: Given Data: The height of the water slide is: h=3.8 m The initial speed of the person is: u=0.70 m/s

Q: In the figure, a stone is projected at a cliff of height h with an initial speed of 49.0 m/s…

A:

Q: A boat travels around a circular path, p = 40m, at a speed that increases with time. The boat has a…

A:

Q: A daredevil is attempting to jump his motorcycle over a line of buses parked end to end by driving…

A: The range of the object is, R=v02 sin2θg   Substitute, R=42.3 m/s2 sin227.7°9.8 m/s2=150.30 m

Q: A jetiner is moving at a speed of 245 m/s. The vertical component of the plane's velocity is 40.6…

A: Given , Speed of plane (v) = 245 m/s Vertical component of plane's speed (vy) = 40.6 m/s sinθ= 0.165…

Q: A projectile is launched directly upward from the surface of the Earth with an initial speed of 5.9…

A: Solution:

Q: A person standing 20.0 meters away from a  wall throws a stone from the ground level  at an angle of…

A:

Q: A rescue plane flying horizontally at 72.6 m/s spots a survivor in the ocean 182 m directly below…

A: Givenux = 72.6 m/suy =0h= 182 max =0ay =5.82 m/s2

Q: If a particle moving in a circular path of radius 4.87 m has a velocity function v = 4t2 (units:…

A: The acceleration of the particle is

Q: An Earth satellite moves in a circular orbit 892 km above Earth's surface with a period of 102.6…

A:

Q: An airplane is cruising at a speed of 257.2 m/s along a straight line and makes a turn along a…

A: Speed, V = 257.2 m/s Centripetal acceleration, ac = 3g = 3×9.8 m/s2 = 29.4 m/s2 Formula for…

Q: A projectile is launched from point A with an initial speed v, = 100 ft/sec. Determine the minimum…

A: Given: Initial velocity=v0=100 ft/sec x-component of velocity=100cosα y-component of…

Q: A bullet is fired from the ground at an initial velocity of 350 m/s and an angle of 50° with the…

A:

Q: A particle changes its velocity at a constant rate from 5 m/s to 8.5 m/s over a time period of 1.2…

A:

Q: A particle is moving along a circular path with tangential acceleration function of a(t) = (0.12t +…

A: Tangential acceleration of particle (a) = 0.12t + 0.3 Radius of curvature = 5.5 m  Velocity at t = 3…

Q: An Earth satellite moves in a circular orbit 878 km above Earth's surface with a period of 102.3…

A: (a) Speed is given by,

Q: An airplane releases a ball as it flies parallel to the ground at a height of h= 285 m as shown in…

A: It is a projectile motion time taken in moving from h height above to bottom is equal to the time…

Q: An experimental jet rocket travels around Earth along its equator just above its surface. At what…

A: The radius of the Earth, r=6.4×106 m   The centripetal acceleration, α=9.8 m/s2

Central Force

Central force is the force that acts along the center of mass of one body to the center of mass of another body. Its direction from or away from a point on a body to another is called the center of the force. Such forces include gravitational force between two massive objects or electrostatic forces between two charged particles. So from atoms to planets, the central forces play an important role in shaping our daily lives. One of the remarkable features of central forces is that they are conservative, i.e. the total energy of a central force system can always be expressed as a gradient of a potential energy function.