Projectile motion question

Question

A projectile is fired from a height of 15 feet with an initial velocity of 240 feet per second at an angle of 45 Degrees with the horizontal. Answer the following questions and round your answers to two decimal places when necessary.

𝑥 = 𝑣𝑜(𝑐𝑜𝑠𝜃)𝑡 and 𝑦 = −16𝑡 2 + 𝑣𝑜(𝑠𝑖𝑛θ)𝑡 + ℎ𝑜

a) What are the simplified parametric equations for the path of the projectile using exact coefficients?

b) What is the total horizontal distance traveled by the projectile?

c) What is the height of the projectile when the horizontal distance is 300 feet?

Answer 1

a) It looks like you have the parametric equations there. Just plug in 45 degrees for theta, 15 feet for h₀, and 240 ft/s for v_0.

b) The first step to find the horizontal distance is to find the total time the projectile spends in the air. This can be done by setting y = 0 and solving for t. (I would do this yourself as well). t≈10.7. Then plug this value of t into the x equation to find the horizontal distance (x), which I found ≈ 1813.8 ft.

c) Simply do the reverse of what you did in the last problem, set x = 0 and solve for t, then plug that into the y equation.