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 AND CHANGE COMBO
- 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_forwardApplication of Newton's second law of motion EF = ma to a 0.5-kg object thrown straight up with an initial velocity of 4 m/s and adopting the sign convention that down is positive results in the following equation: mg - 2v = ma. What is the velocity v of the object as a function of t? Select the correct response: v = 2.45 - 6.45 exp (-4t) O v = 2.45 - 1.55 exp (-4t) O v = 2.45 + 1.55 exp (-4t) V = 2.45 + 6.45 exp (4t)arrow_forward
- A 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_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_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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