Final answer:
To calculate the height of the cliff, we determine the initial vertical velocity and the vertical displacement using physics equations for projectile motion, considering the given initial velocity, angle, and time of flight, then add the initial height from which the arrow was shot.
Step-by-step explanation:
To find the height of the cliff that an arrow lands on after being shot from a height of 1.6 meters with an initial velocity of 27 m/s at an angle of 60° to the horizontal, we'll use kinematic equations for projectile motion. Given that the time of flight is 3.99 seconds, we can determine the vertical position of the arrow when it lands.
First, we calculate the initial vertical velocity (uy) and the vertical displacement (sy) using the following equations:
- uy = u × sin(θ) = 27 m/s × sin(60°)
- sy = uy × t + 0.5 × g × t2 = (uy × 3.99 s) - 0.5 × 9.81 m/s2 × (3.99 s)2
After calculating uy and subsequently sy, we add the initial height of 1.6 m to sy to get the total height reached above the ground level. The sum gives us the height of the cliff.