Answer:
We can solve this problem using kinematic equations of motion, assuming that air resistance is negligible. We can break the initial velocity of the pumpkin into horizontal and vertical components:
v₀x = v₀ cosθ = 60 cos40° = 45.8 m/s
v₀y = v₀ sinθ = 60 sin40° = 38.4 m/s
Since there is no vertical acceleration after launch, we can use the following kinematic equation to find the time of flight:
Δy = v₀y t + 1/2 a t²
where Δy is the vertical displacement of the pumpkin, a is the acceleration due to gravity (-9.81 m/s²), and t is the time of flight. When the pumpkin lands on the ground, its vertical displacement is zero, so we can solve for t:
0 = v₀y t + 1/2 a t²
t = -2v₀y / a = -7.82 s
This negative value indicates that the pumpkin lands on the ground after 7.82 seconds, which makes physical sense. Now, we can use the horizontal velocity to find the horizontal distance traveled during the time of flight:
Δx = v₀x t = 45.8 m/s * 7.82 s = 358.2 m
Finally, we can find the total speed of the pumpkin at landing by using the Pythagorean theorem:
v² = v₀x² + v²y
v = sqrt[(v₀x)² + (v₀y)²] = sqrt[(45.8 m/s)² + (38.4 m/s)²] = 60.0 m/s (approximately)
Therefore, the answer is D) 60 m/s.
Step-by-step explanation: