physics help needed please?

Question

In lab situations, a projectile range can be used to determine its speed. To see how high this is done, supose a ball rolls off a horizontal tabke and lands 1.5 m out from the edge of the tabke. If the table top is 90cm above the floor, determine a) the time the ball is in the air,and b) the balls speed as it left the table top.
What????? please help!

Answer 1

Use your two demensional projectile motion equations

y = vertical
x= horizontal

y= v(initial)t + 1/2at^2
x = v(initial)t + 1/2at^2


y = .9 m above the ground
x = 1.5 m from the edge of the table

we know that gravity is 9.8 m/s^2 so we can plug that into our y equation because the acceleration in a vertical direction toward earth will always be this. We also know that the starting velocity in the y direction is 0 because it is not moving downward until it has rolled off the table. this allows you to cancel out the v(initial)t term in the y equation leaving you with 1/2(9.8)t^2

So where do we get t??

well .9 = 1/2(9.8)t^2
so... take the square root of .9/(.5)(9.8)

now that you have your time, lets find out how fast it was going. Lets do some canceling first...we know that there is no force of acceleration on the ball in the horizontal direction (x direction) so our acceleration will be 0. This cancels out the 1/2at^2 term and leaves you with 1.5 = vt
Plug in your value for t and solve for v.

That v value is how fast it was going when it left the table

Answer 2

a. To solve for the time use the formula,

s=ut+1/2at^2

Where s is the distance travelled in m, a the acceleration of gravity in m/s^2, and t the time in s (seconds).

If we take the vertical direction, s=90cm or 0.9m, u is 0 since the ball rolls off a horizontal table, and a=9.8m/s^2.

Substitute known values:

0.9=0*t+1/2*9.8t^2
t^2=0.9/4.9
=0.18
t =.43s

b. To solve for the ball speed, we use the basic formula,

D=r*t

Where D is the horizontal distance traveled in m, r is the ball speed as it left the table, and t is the time of travel of 0.43s.

Given: D=1.5m

Substitute known values:

1.5=r*0.43
r=1.5/0.43
r=3.48m/s

Note: In the horizontal direction, the speed is constant. The acceleration of gravity does not enter into the equation. Just use the basic formula, distance=speed*time formula given above.