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?

h = 90.09 m

Explanation:

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

where,

X = horizontal distance covered = 150 m

Vₓ = Horizontal component of velocity = 35 m/s

t = time taken during the motion = ?

Therefore,

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

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 = 90.09 m

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