A ball is thrown vertically upward with a speed of 11.0 m/s. (a) How high does i

Question

A ball is thrown vertically upward with a speed of 11.0 m/s.
(a) How high does it rise?
m

(b) How long does it take to reach its highest point?
s

(c) How long does the ball take to hit the ground after it reaches its highest point?
s

(d) What is its velocity when it returns to the level from which it started?
m/s

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Explanation / Answer

a) Note that, at maximum height, v_f = 0. Using (v_f)^2 = (v_i)^2 + 2ad, we see that: 0 = (v_i)^2 + 2ad ==> d = -(v_i)^2/(2a) = -(11.0 m/s)^2/[2(-9.8 m/s^2)] = 6.17 m. (b) Since v_f = 0 at maximum height, we see that: v_f = v_i + at ==> t = -v_i/a = -(11.0 m/s)/(-9.8 m/s^2) = 1.12 s. (c) Since the time it takes for the ball to get from the ground to max height is the same as the time it takes for the ball to reach from max height to the ground, we see that the ball is in the air for: 2(1.12 s) = 2.24 s. (d) Using v_f = v_i + at, we see that the velocity of the ball is: v_f = (0.00 m/s) + (9.8 m/s^2)(1.12 s) = 11.0 m/s.

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