Question

5) Starting from rest, a car accelerates at a constant rate, reaching 88 km/h in 17 s. (a) Find its acceleration. (b) Find how far does it goes in this time.

6) A delivery drone drops a well-cushioned package from a height of 15.7 m onto a customer’s porch. At what speed does the package hit the porch?

7) A diver drops from a 7.44-m high cliff. (a) At what speed does she enter the water? (b) How long is she in the air?

8) A foul ball leaves the bat going straight upward at 22 m/s. (a) How high does it rise? (b) How long is it in the air? Neglect the distance between the bat and the ground.

Answer 1

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5. a) Converting speed from km/h to m/s , speed = 88 * 5/18 = 24.44 m/s

Acceleration = (v - u ) / t , where v is final velocity, u is initial velocity, t is time taken

Therefore a = (24.44 - 0) / 17 = 1.43 m/s^2

b) Distance covered = u*t + 0.5 * a* t^2 = 0 + 0.5*1.43*17*17 = 206.35 m

6 ) Taking downward direction as positive,

and using v^2 = u^2 + 2* a *s

u = 0 (since dropped from rest)

v^2 = 2 * g * 15.7 = 314

v = 17.7 m/s

7 . a ) Again using previou formula ,

v^2 = 2 * 10 * 7.44

v = 12.19 m/s

b ) Using s = u*t + 0.5*a*t^2

7.44 = 0 + 0.5 * 10 * t^2

t = 1.22 sec

8 . Taking upward direction as positive.

a ) and using v^2 = u^2 + 2* a * s

v = 0 (at highest point, velocity is 0) , u = 22 m/s , a = -10 m/s^2 (g is acting downwards)

0 = 484 - 2 * 10 * s

s = 24.2 m

b ) Using v = u + a*t

0 = 22 - 10 * t

t = 2.2 seconds