Question

Batman is 6.22 m from the

base of a building when he
shoots a grappling hook at
29.9 m/s up towards a
ledge at a 52.2° angle.
What is the height of the
ledge when the hook
attaches?

Answer 1

To find the height of the ledge when the hook attaches, we need to use the following kinematic equation:

y = y0 + v0y*t - 1/2*g*t^2

where:
y = final height of the ledge
y0 = initial height of the hook
v0y = initial vertical velocity of the hook
g = acceleration due to gravity
t = time taken for the hook to reach the ledge

First, we need to find the initial vertical velocity of the hook:

v0y = v0*sin(theta)
where:
v0 = initial velocity of the hook = 29.9 m/s
theta = angle of elevation = 52.2 degrees

v0y = 29.9*sin(52.2) = 23.2 m/s

Next, we need to find the time taken for the hook to reach the ledge:

y = y0 + v0y*t - 1/2*g*t^2
At the top of the trajectory, the vertical velocity of the hook will be zero, so we can write:

0 = v0y - g*t
t = v0y/g

t = 23.2/9.81 = 2.36 s

Finally, we can use the kinematic equation to find the height of the ledge:

y = y0 + v0y*t - 1/2*g*t^2

y = 6.22 + 23.2*2.36 - 1/2*9.81*2.36^2

y = 6.22 + 54.8 - 28.0

y = 32.0 m

Therefore, the height of the ledge when the hook attaches is 32.0 meters.