Hammer Projectile Motion: Time and Range Calculations.

[joemama69]

Homework Statement

A worker on the roof of a house drops his hammer, which slides down the roof at a constand speed of 4 m/s. The roof makes an angle of 30 degrees with the horizontal, and its lowest point is 10 m from the ground.

A-find the time it takes to hit the ground
b- what is the range

Homework Equations

v(x) = 4cos-30 = 3.464
v(y) = 4sin-30 = -2

The Attempt at a Solution

Just want someone to verify my work

y = y(initial) + v(y)t + .5gt
0 = 10 - 2t - 4.9t, t = 1.239s

x = x(initial) + v(x)t
x = 3.464(1.239) = 4.291 m

 

[rl.bhat]

Your solution is correct.
But in the equation
y = y(initial) + v(y)t + .5gt
it should by
y = y(initial) + v(y)t + .5gt^2

 

[tomcue]

Your calculations appear to be correct. In order to verify your results, we can also use the equation for range in projectile motion, which is R = v(initial)^2 * sin(2θ)/g. Plugging in the given values, we get R = (4)^2 * sin(60)/9.8 = 4.291 m, which matches your result. Additionally, we can also use the equation for time of flight, which is t = 2v(initial)sin(θ)/g. Plugging in the given values, we get t = 2(4)sin(30)/9.8 = 1.239 s, which also matches your result. Therefore, your calculations are correct.