Concept explainers
Reminder Round all answers to two decimal places unless otherwise indicated.
Looking Up The constant
(We measure upward velocity
a. Use a formula to express the velocity
b. How many seconds after the toss does the rock reach the peak of its flight? (Hint: What is the velocity of the rock when it reaches its peak?)
c. How many seconds after the toss does the rock strike the ground? (Hint: How aces me time it takes for the rock to rise to its peak compare with the time it takes for it to fall hack to the ground?)
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FUNCTIONS+CHANGE -WEBASSIGN
- Skidding in a Curve A car is traveling on a curve that forms a circular arc. The force F needed to keep the car from skidding is jointly proportional to the weight w of the car and the square of its speed s and is inversely proportional to the radius r of the curve. a Write an equation that expresses this variation. b A car weighing 1600 lb travels around a curve at 60 mi/h. The next car to round this curve weighs 2500 lb and requires the same force as the first car to keep from skidding. How fast is the second car traveling?arrow_forwardRipples in a pond When a stone is thrown into the center of a pond, the ripples spread out in a circular pattern, moving at a rate of 3 feet per second. If the stone is dropped at a point (0,0) in the illustration, when will the ripple reach the seagull floating at the point (15,36)?arrow_forwardYOUR TURN Find the velocity and acceleration of the car if the distance in feet is given by s(t)=t33t224t+10, at time t in seconds. When is the car going forward or backing up? When is the car speeding up or slowing down?arrow_forward
- Doctors treated a patient at an emergency room from 2:00P.M. to 7:00P.M. The patient’s blood oxygen level L (in percent) during this time period can be modeled by L=0.270t2+3.59t+83.1,2t7 where t represents the time of day, with t=2 corresponding to 2:00P.M. Use the model to estimate the time (rounded to the nearest hour) when the patient’s blood oxygen level was 93 .arrow_forwardThe following problems review material we covered in Section 3.5. Linear Velocity A point moving on the circumference of a circle covers 5 feet every 20 seconds. Find the linear velocity of the point.arrow_forwardA ball is thrown vertically up from the ground. If the positive direction is upward, then h= - 167 – 321 feet gives the height of the ball after t seconds. An observer is 20 feet from the point where the ball was thrown. Find the rate at which the distance between the ball and the observer changing after 2 seconds. Round- off your answer to 2 decimal places. Blank 1 feet per second Blank 1 Add your answerarrow_forward
- Directions: Answer the following problems. Show your complete solutions. 1. if a stone is thrown vertically upward from the surface of the moon with a velocity of 10 meters per second (m/s), its height (in m) after t seconds (s) is h= 10t - 0.83t2. a. What is the velocity of the stone after 3 s? b. What is the velocity of the stone if it has risen by 25 m?arrow_forwardThe water level in a tank rises 4 feet every minute. Write an equation of change that describes the height H, in feet, of the water level at time t in minutes.a. dH/dt = 3b. dH/dt = 4c. dH/dt = 5d. dH.dt = 6arrow_forwardEXAMPLE 5 A man walks along a straight path at a speed of 4 ft/s. A searchlight is located on the ground 6 ft from the path and is kept focused on the man. At what rate is the searchlight rotating when the man is 8 ft from the point on the path closest to the searchlight? SOLUTION We draw the figure to the left and let x be the distance from the man to the point on the path closest to the searchlight. We let A be the angle between the beam of the searchlight and the perpendicular to the path. We are given that de = 4 ft/s and are asked to find d/at when x = 8. The equation that relates x and A can be written from the figure: - tan A Video Example ) tan A Tutorial Online Textbook Differentiating each side with respect to t, we get dx dA -- 6 sec'(A) dt dt so dA 1 dx 1 *(4) dt 6 dt 6 cos (A) When x = 8, the length of the beam is 10, so cos(A) = /10 = and dA dt The searchlight is rotating at a rate of rad/s.arrow_forward
- Student PROJECT A Parachutist in Free Fall Figure 1.30 Skydivers can adjust the velocity of their dive by changing the position of their body during the free fall. (credit: Jeremy T. Lock) Julie is an avid skydiver. She has more than 300 jumps under her belt and has mastered the art of making adjustments to her body position in the air to control how fast she falls. If she arches her back and points her belly toward the ground, she reaches a terminal velocity of approximately 120 mph (176 ft/sec). If, instead, she orients her body with her head straight down, she falls faster, reaching a terminal velocity of 150 mph (220 ft/sec). Since Julie will be moving (falling) in a downward direction, we assume the downward direction is positive to simplify our calculations. Julie executes her jumps from an altitude of 12,500 ft. After she exits the aircraft, she immediately starts falling at a velocity given by v(t) = 32t. She continues to accelerate according to this velocity function until she…arrow_forwardCourse search Mahmood A ty of Technology and Applied Sciences Ibri The position of a moving particle is given by s = t- 8t + 15, then its speed at t = 8 is O 10 age ouncements Jump to... gation OO0 Oarrow_forward
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