An object is fired straight upward from ground level with an initial velocity of

Question

An object is fired straight upward from ground level with an initial velocity of 22m/s. It reaches the top of the flight and then fall back to ground level. You may neglect air resistance.



A) How long will the object be in the air?

B) What maximum height above the ground will be reached by the object?

C) What is the acceleration of the object at the top of the flight?

D) The object passes through a height of 8 meter above the ground twice during this motion. Find the two times when this happen. As always, you can assume that the time starts when the object is launched.

time 1=__________ second

time 2___________ seconds

Explanation / Answer

You can think of this problem like tossing a ball in the air straight up and down.

Based on the problem, we know two things immediately: initial velocity and acceleration.

vi=22 m/s and a=-g=-9.8 m/s2

A) To solve this equation you need to understand the idea that the ball will intially be moving upward until i changes directions and begins to fall. in that instant, the velocity is zero. so we use the eqn:

v=vi+at

v-vi=at

(v-vi)/a=t

(0-22)/-9.8=t

t=2.245 seconds

now that, in words, means the time it takes for the ball to accelerate negatively to a velocity of zero, which would be the time it take to reach the top. without going into too much detail, the time it takes to go up equals the time it takes to go down, so the total time, T, is 2t

T=2t=4.49 s

B) This it simply a plug and chug eqn:

h=v0t+.5at2

note however, that to find maximum height we use the value of t. this value represents the time it takes to reach maximum height

h=22(2.245)+.5(-9.8)(2.2452)=24.7 m

C) This question is conceptual. the acceleration throughout the enitre problem is constant and is -9.8 m/s2

D) This part is tougher. to solve it, use the same equation from B)

h=v0t+.5at2 except this time, plug in 8 m for h and solve for t using the quadratic formula.

saving you the time however, t=0.4 s and 4.09 s

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