physics speed and kinetic energy?

Question

5. A 0.9 kg rock slides horizontally off a table
from a height of 1.4 m. The speed of the rock
as it leaves the thrower's hand at the edge of
the table is 1.7 m/s, as shown.
The acceleration of gravity is 9.81 m/s^2 :
How much time does it take the rock to
travel from the edge of the table to the floor?
Answer in units of s.
part2
What is the kinetic energy of the rock just
before it hits the floor? Answer in units of J.

Answer 1

Since I can't see the diagram on your homework question, I assume the thrower is sliding the rock horizontally across the table (at which point it falls off the edge, having 1.7m/s horizontal velocity)

For part 1:
Let V be the vertical speed of the rock falling
Let A be the acceleration to gravity (9.81 m/s^2)
Let T be time in seconds (T=0: rock goes over edge)
Let H be the height of the rock, in meters
Let H' be the initial height of the rock (the table's height)

Start with a simple velocity equation. Velocity equals Time multiplied by Acceleration.

V=TA

This is how fast the object is moving, but we want to know it's position. The best way to do that is integrate over time T. Note that when you integrate, there can be an initial constant that you have to add back in: in this case, it's the height of the table)

H=H' - (T^2A) / 2

(This says: "the height of the rock at any time T equals the initial height of the rock, minus T squared multiplied by A, divided by 2")

Well, we care about H=0 -- that's when the rock hits the floor. Substitute!

0=H' - (T^2A) / 2

Move stuff around in the equation:

(T^2A)/2 = H'

The rest is left for you (Hint, you would like T)

Part 2:
Lets pretend you have T from part 1 (the # of seconds it takes for the rock to hit the floor). I'll call that.... T.

Going back to part 1 again:

V=TA

"V" in this case is the vertical speed. Lets rename it to "Vy", to be the vertical component of velocity (remember Velocity is Speed AND Direction)

Vy=TA

Pretty easy to get Vy now, as you have T from part 1, and A which is fixed.

Lets look at Vx (the horizontal component of the velocity). That's pretty simple, it's given to us: 1.7 m/s

Lets get the speed of the object (remember, the object is travelling TA m/s downwards, and 1.7 m/s horizontally)

S = sqrt(Vx^2 + Vy^2)

Now that you have the speed S of the the object just before it hits the floor, you can easily get the kinetic energy.

Answer 2

1/2 mass X velocity squared = Kinetic Energy

Answer 3

What do you mean Throwers?

Answer 4

just copy and paste in to google.

Answer 5

3.21s & 6.65J...come on this is too easy!