Question

Abunai Hana is standing atop a hill and fires her crossbow perfectly horizontally. If the crossbow bolt begins

moving with a speed of 35 m/s, then at what height does the bolt land if it hits the ground 150 m horizontally

away from her?

Answer 1

h = 90.09 m

Step-by-step explanation:

First, we consider the horizontal motion of the crossbow. Considering air friction to be negligible we can use the following equation:

`X = V_(x)t`

where,

X = horizontal distance covered = 150 m

Vₓ = Horizontal component of velocity = 35 m/s

t = time taken during the motion = ?

Therefore,

`150\ m = (35\ m/s)t\\\\t = (150\ m)/(35\ m/s)\\\\t = 4.28\ s`

Now, we consider the vertical motion of the crossbow. Using second equation of motion:

`h = V_(i)t + (1)/(2)gt^(2)\\\\`

where,

h = the height the bolt fell = ?

Vi = Vertical component of initial velocity = 0 m/s (since the crossbow was fired horizontally)

g = acceleration due to gravity = 9.81 m/s²

Therefore,

`h = (0\ m/s)(4.28\ s) + (1)/(2)(9.81\ m/s^2)(4.28\ s)^(2)\\`

h = 90.09 m