# Calculating the horizontal distance traveled of an object that was thrown.

A ball is thrown up onto a roof, landing 3.70s later at height h = 21.0m above the release level. The ball's path just before landing is angled at θ = 54.0˚ with the roof.
Find the horizontal distance it travels.

Related Equations:
Xf = Xo + 1/2(Vf + Vo)t
_____________________

My approach on this problem was to find the velocity the moment before impact with the roof and to use basic trigonometry to calculate the horizontal velocity of the ball. From the given facts I can infer that:

Xf = 21m
Xo = 0m
t = 3.70s
Vo = ?
Vf = Vo*sin(54)

Now, plugging this into the equation above I get:
21 = 1/2(Vo*sin(54) + Vo)3.70
42 = (Vo*sin(54) + Vo)3.70
11.35 = .81Vo + Vo
11.35 = 1.81Vo
6.27 = Vo

With Vo I can calculate the horizontal velocity which would be:
Vx = Vo*cos(54)
Vx = 6.27(.59)
Vx = 3.69

And the distance should therefore be:
d = VxT
d = 3.69(3.70)
d = 13.65

However, the answer is not 13.65m and after scratching my head and approaching this problem through multiple, yet similar, angles I finally decided to ask for help. Can somebody help me and point out what I did wrong? I thought I had the right idea but I can't seem to get the right answer?

Thank you for taking the time to read my question.
Sincerely David A.P.

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dave, can you write the original question AS IT IS. its not clear how the ball is flying. was it thrown vertically upwards or what ? also when it lands on the roof, which angle the $\theta$ is ? a pic will help

Sure! Here's an image that came with the problem. However, the wording is nearly identical to the problem itself. gneill
Mentor
Concentrate on the vertical motion first. Rather than clutter things with the sine and cosine functions from the outset, just assume that the initial vertical velocity is vyo. Can you solve for it using one of the common kinematic equations from what you're given?

gneill
Mentor
hi david

here's how i would do it.
[SNIP ALL]

issacnewton, it is a Physics Forums rule that helpers NOT simply solve homework problems and present complete solutions. Posters must do their own work, with help, hints, and guidance provided as required. Breaking the rule can get one banned from PF.