# A ball is thrown vertically upward with a speed of 17.0 m/s. (a) How high does i

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A ball is thrown vertically upward with a speed of 17.0 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
May 25th, 2015

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May 25th, 2015

We can use the equation:

s(t) = (-1/2)at^2 + v₀t + s.

Assuming that we are talking about Earth's atmosphere (and which a = -9.8) and s = 0, this becomes:

s(t) = -4.9t^2 + 17t.

From here, part a) can be solved by finding the y-coordinate of the vertex, part b) can be solved by finding the x-coordinate of the vertex, the answer to part c) is the same to that as part b) as it takes the same amount of time for it to fall back down, and part d) can be solved by differentiating and finding the slope of the tangent line at the point the ball hits the ground.

I hope this helps!

May 25th, 2015

(a) V² = U² +2*a*s
0 = 17² + 2*(-9.81) *s
0 = 289- 19.62*s
19.62s = 289
s = 289/19.62
s = 14.73 m
Height achieved = 14.73 m

b) V = U + a*t
0 = 17 + (-9.81) t
9.81t = 17
t = 1.73 seconds.

c) Time up = time down

d) It will hit the ground with the same velocity with which it was thrown = 19 m/s

May 25th, 2015

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May 25th, 2015
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May 25th, 2015
Nov 25th, 2017
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