A projectile is thrown horizontally at 11.8 m/s.The projectile hits the ground 0.51 s later.What is the angle of impact the projectile makes with the horizontal ground?

A) -25.1°
B) -23°
C) 115.1°
D) -89.7°
E) -67°

Question

A projectile is thrown horizontally at 11.8 m/s.The projectile hits the ground 0.51 s later.What is the angle of impact the projectile makes with the horizontal ground?
​
A) -25.1°
B) -23°
C) 115.1°
D) -89.7°
E) ​-67°

Quizplus · Accepted Answer

Since the projectile is thrown horizontally, its initial vertical velocity is 0 m/s. Using the formula d = V₀t + ½at², where d is the vertical distance traveled, V₀ is the initial velocity, t is the time in seconds, and a is the acceleration, we can find the distance the projectile falls before hitting the ground:

d = 0.5 * 9.81 m/s² * (0.51 s)² = 1.26 m

Next, we can find the horizontal distance traveled by the projectile using the formula d = vt, where d is the horizontal distance, v is the horizontal velocity, and t is the time:

d = 11.8 m/s * 0.51 s = 6.018 m

Now we can find the angle of impact using the formula tanθ = opposite/adjacent, where θ is the angle, opposite is the vertical distance, and adjacent is the horizontal distance:

tanθ = 1.26 m / 6.018 m
θ = atan(1.26 m / 6.018 m) = -23° (since the projectile hits the ground to the left of the launch point, the angle is negative)

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