Question

1. A baseball is hit so that it travels straight upward after being struck by the bat. A fan observes that it takes 3.20 s for the ball to reach its maximum height.
(a) Find the ball's initial velocity.
(b) Find the height it reaches.

2. The driver of a car slams on the brakes when he sees a tree blocking the road. The car slows uniformly with acceleration of -5.40 m/s² for 4.30 s, making straight skid marks 64.6 m long, all the way to the tree. With what speed does the car then strike the tree?

3. A truck covers 39.0 m in 8.10 s while smoothly slowing down to final speed of 2.10 m/s.

(b) Find its acceleration. (Indicate the direction of the acceleration with the sign of your answer.)

Answer 1

1.

a) using 1st equation of motion

u = gt

u = 9.8* 3.2 = 31.36 m/s

b)

h = ut - 0.5 gt^2

h = 31.36* 3.2 - 0.5*9.8* 3.2^2

h = 50.176 m

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2.

using 2nd equation of motion

d = ut - 0.5* at^2

64.6 = u* 4.3 - 0.5* 5.4* 4.3^2

u = 26.633 m/s

using 1st equation of motion

v = u - at

v = 26.633 - 5.4* 4.3

v = 3.41 m/s

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3.

using 2nd equation of motion

d = ut - 0.5 at^2

39 = 8.1 u - 0.5* a* 8.1^2

8.1 u - 32.805 a = 39 (i)

using 1st equation of motion

v = u - at

2.1 = u - 8.1 a (ii)

solving (i) and (ii)

u = 7.082 m/s

a = 0.56 m/s^2

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