How do you solve the following physics problem?

[federox]

Determine the initial velocity of a projectile that is launched horizontally, and falls 1.5 m while moving 16 m horizontally.
Thanks!

[Jesse_J]

You have to evaluate this problem with respect to both the x and y motions. We know that it falls 1.5m. Acceleration due to gravity is 9.8 m/s^2. We can use our kinematics equation for distance to find the initial velocity. The equations vf=vi+at, sf=si+vi*t+1/2at^2, and vf^2=vi^2+2a(delta s) will help us. We plug in the values for the second equation to get final velocity = sqrt(2*9.8*1.5m) = 5.42 m/s when it hits the ground. Then we can solve for time to fall using the first equation, 5.42=0+9.8t, t= .55 seconds. Then lastly plug in the known values to find initial velocity using the second equation, 16m=0+x*.55-1/2(9.8 )(.55)^2. x=31.8 m/s.

[ricki]

d = vt + (1/2)at^2

1.5 = 4.9t^2

t = 0.55 sec

horizontal v = 16/0.55 = 29.1 m/s