Answer:
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:
[tex]X = V_{x}t[/tex]
where,
X = horizontal distance covered = 150 m
Vₓ = Horizontal component of velocity = 35 m/s
t = time taken during the motion = ?
Therefore,
[tex]150\ m = (35\ m/s)t\\\\t = \frac{150\ m}{35\ m/s}\\\\t = 4.28\ s[/tex]
Now, we consider the vertical motion of the crossbow. Using second equation of motion:
[tex]h = V_{i}t + \frac{1}{2}gt^{2}\\\\[/tex]
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,
[tex]h = (0\ m/s)(4.28\ s) + \frac{1}{2}(9.81\ m/s^2)(4.28\ s)^{2}\\[/tex]
h = 90.09 m
