physics homework

Question

You are watching your friend play hockey. In the course of the game, he strikes the puck in such a way that, when it is at its highest point, it just clears the surrounding 2.80 m high Plexiglas wall that is 11.7 m away. (Ignore any effects due to air resistance.)

(a) Find the vertical component of its initial velocity. 

v_0y =  ?m/s 

(b) Find the time it takes to reach the wall. 

Δt = ? s 

(c) Find the horizontal component of its initial velocity, and its initial speed and angle. 

v0x	=  ? m/s
v0	=  ? m/s
𝜃	=  ? °

Answer 1

Let

x₁ = 11.7 m be the horizontal distance the puck travelled,

y₁ = 2.8 m be the vertical distance the puck travelled,

Δt be the time the puck travelled to the point (x₁, y₁),

g = 9.81 m/s² be the gravitational acceleration,

v_0x be the x-component of the puck's initial velocity,

v_0y be the y-component of the puck's initial velocity.

The puck horizontal movement is not subject to any acceleration, and therefore

its horizontal velocity remains v_0x, and

x₁ = v_0xΔt (1)

The puck's vertical movement is subject to gravitational acceleration,

causing its initial v_0y to decrease to 0:

v_0y = gΔt (2)

The distance traveled is

y₁ = gΔt²/2 (3)

From (3)

Δt = √(2y₁/g) (4)

(a)

From (2) and (4)

v_0y = g√(2y₁/g) = √(2y₁g) = √(2 × 2.8 m × 9.81 m/s²) = 7.4 m/s

(b)

Δt = √(2y₁/g) = √(2 × 2.8 m / 9.81 m/s²) = 0.76 s

(c)

From (1)

v_0x = x₁/Δt = 11.7 m / 0.76 s = 15.4 m/s

Initial speed, being the length of the velocity vector

= √(v_0x² + v_0y²) = √(15.4² + 7.4²) = 17 m/s

θ = arctan(v_0y/v_0x) = arctan(7.4/15.4) = 25.7°