Thread: Story Problem

A ball is thrown at a velocity of 16ft/sec off the top of a roof 320 feet above the ground.

a) Use the formula s=-16t^2 + v0t +s0 to write the equations which describes the height of the ball above the ground, s, in t seconds after the fall begins.

s=-16t^2 + 16t +320

b) How long will it take the ball to hit the ground?

How do I figure out the answer for part b?

You simply have to make t the subject by using the " completing the square " method.

Hence, step by step,

=> s= -16t^2 + 16t +320

=> -s = 16t^2 - 16t - 320

=> -s = (4t)^2 - 2(8)t - 320

Note: (4t - 8)^2 = 16t^2 - 16t + 64 || compare -s+320: 16t^2 - 16t
the excess is 64, right? simply, minus 64.

=> -s = (4t - 8)^2 - 320 - 64

Now, to make t the subject,

=> -s + 64 + 320 = (4t - 8)^2

=> (4t - 8) = (-s + 64 + 320)^(1/2)

=> t = (1/4)[8 + (-s + 64 + 320)^(1/2)]

In the end, you simply have to sub the values, and you have t ( time taken for the ball to hit the ground ).

since s is defined as the height of the ball above the ground, then s = 0 when it hits ground.

=> t = (1/4)[ 8 + (0 +64 + 320 )^(1/2)] = 6.90 ( 3.s.f )

Hm, not really sure, but note that the question gives hint to what s.f it wants, and basing on the values they give 16 and 320, it could want the answer in 2.s.f; hence,

t = 6.898979 ... = 6.9 ( 2.s.f )

Hence, time taken for the ball to hit the ground is 6.9s.