Final answer:
To find the height of the cliff, the vertical component of the arrow's initial velocity is calculated, and then the basic kinematic equation for vertical motion is used. After calculating, we find that the arrow lands on a cliff that is approximately 27.02 m high, and the closest provided option is 28 m.
Step-by-step explanation:
Calculating the Height of the Cliff
To calculate the height of the cliff, we use the basic kinematic equation for vertical motion since the arrow's vertical velocity component affects the height it reaches. The vertical component of the initial velocity (Vy) can be found using the formula Vy = V * sin(θ), where V is the arrow's initial velocity and θ is the angle of projection. Here, V = 30 m/s and θ = 60°.
Vy = 30 m/s * sin(60°) = 30 m/s * (√3/2) = 25.98 m/s approximately.
The equation h = h0 + Vy * t - 0.5 * g * t² will give us the height H when the arrow lands on the cliff. Here, h0 is the initial height from which the arrow is shot, t is the time of flight, and g is the acceleration due to gravity (approximately 9.8 m/s²).
Using the given values, h0 = 1.5 m, t = 4 s, we get:
H = 1.5 m + (25.98 m/s * 4 s) - 0.5 * 9.8 m/s² * (4 s)²
H = 1.5 m + 103.92 m - 78.4 m
H = 27.02 m (approximately).
Since none of the options a. 28 m, b. 34 m, and c. 38 m exactly match our calculated result (and we have rounded our calculations), the most suitable answer based on the provided options would be (a) 28 m, as it is the closest value.