How Fast Are Romeo's Pebbles When They Hit Juliet's Window?

[SnowOwl18]

Ok...here's another problem that i keep getting wrong:

*Romeo is chucking pebbles as gently as he can up to Juliet's window. That is, he wants the pebbles to hit the window with the least possible speed...He is standing at the edge of a rose garden at H = 7.70m below her window and at D = 8.90m from the base of the wall. How fast are the pebbles going when they hit her window?*

Ok, so the horizontal component is 8.9m and the vertical is 7.7m...I tried
- tan= 7.7/8.9 to get theta and then use that to get the hypoteneuse, but i realized, after getting the problem wrong, that I only got the distance of the hypoteneuse, when i really needed the velocity...so how would i find that? thanks for any help

 

[Sirus]

Also remember that the pebbles would follow a projectile (parabolic) path, not a triangular path, due to the effect of gravity. Ignoring air friction (which is not present in this problem), the horizontal velocity of the pebbles will stay constant throughout their trajectory. Where in a parabolic path will the vertical velocity of the pebbles be the least?

 

[M98Ranger]

To find the velocity, you will need to use the equation for projectile motion: V = √(V0^2 + 2ad), where V0 is the initial velocity, a is the acceleration (in this case, due to gravity which is -9.8 m/s^2), and d is the distance traveled (8.9m in the horizontal direction). To find V0, you can use the equation V0 = Vcosθ, where θ is the angle you found using tan^-1(7.7/8.9). Plug in these values into the first equation and you should be able to solve for the velocity. Remember to use the negative value for a since it represents the downward direction. Hope this helps!