Throwing Rocks: Analyzing Horizontal & Vertical Motion

[liz777]

Homework Statement

A rock is thrown at an angle of 17 degrees above the horizontal at 28.5 m/s, from the ground.

a)How high will the rock rise above the ground?
b)What is the horizontal speed of the rock at the top of its flight?
c) How long will it take the rock to reach a vertical speed of zero m/s?

The Attempt at a Solution

First I found out what the x and y components are. x=27.25 m/s and y=8.35 m/s. Then I found the time w/ vf=vi+at. (27.25=9.8t)

a)I used the formula d=vit+1/2at^2 and it came out to 37.87 m
=1/2(9.8)(2.78)^2
b) I'm guessing I would use the formula v=d/t. So the max height is 37.87 and the time is 2.78(1/2 the time of the rock's total air time). and I got the answer 13.62 m/s
c) I wasnt really sure on this one. Is it 2.78s, when the ball is at the top of its flight?

Any advice/help would be great. I want to make sure I'm doing this correctly. Thanks! :)

 

[casedogg]

The horizontal velocity never changes

 

[Trentonx]

This equation will be helpful
The vertical position with respect to time is given by
y(t) = y_0 + (V_0)t-4.9t^2
V_0 in the y direction is V_0sin(theta)
so 28.5sin(17)
where y'(t) = 0, the projectile has reached it's max height. Put that t into the y(t) to find the maximum height. This should also be the answer for c)
velocity in the x direction is V_0cos(theta)
so 28.5cos(17). As casedogg said, it doesn't change.