An object is launched upward with an initial velocity of 64 feet per second from a platform 80 feet high.How long will it take for the object to hit the ground?

Question

I need help with this problem badly!

Answer 1

To solve physics problems it helps to start writing down the knowns and unknowns and coordinate axis.  

 

Let's set y as up/down

 

Vy=64 ft/s (initial velocity in the y direction)

Dy=80 ft (distance in the y direction)

 

Solve for time (t)

 

The fastest way is to use a distance formula that is dependent on time:

 

yfinal=yinitial+Vy*t+.5*g*t^2 

 

if we do a simple subtractions we get

 

0=(yinitial-yfinal)+Vy*t+.5*g*t^2  (it is important that all of the variables are in terms of y since x is independent and requires a whole new equation)

yintial-yfinal= Dy or the 80 ft the object will fall

Now we substitute all the knowns

 

0=80+64*t-.5*32.2*t^2

 

Since the problem does not consist of whole integers factoring is difficult and the quadratic formula would be easiest

t=(-64±(64^2+4*16.1*80)^(1/2))/-32.2

From this we get two answers

t=4.97 and -.999 s

Negative time makes no sense so the answer is 4.97 s.