You shoot an arrow with a mass of 0.54 kg at 45º above the horizontal.The bow exerts a force of 125 N for 0.65 s.With no air resistance,the maximum height the arrow reaches is
A)1.2 km
B)5.4 m
C)0.57 km
D)0.29 km
E)0.61 km

Question

Quizplus · Accepted Answer

First, we need to find the initial velocity of the arrow using the force applied by the bow.

F=ma

125 N = 0.54 kg * a

a = 231.5 m/s^2

We know that the bow exerts this force for 0.65 s, so we can calculate the final velocity of the arrow:

v = at

v = 231.5 m/s^2 * 0.65 s

v = 150.5 m/s

Using the initial velocity and the angle of 45º, we can find the vertical and horizontal components of the velocity:

vy = v * sin(45º) = 106.1 m/s

vx = v * cos(45º) = 106.1 m/s

The time it takes for the arrow to reach its maximum height is equal to the time it takes for the vertical velocity to become zero:

vy = 0 = v0y + at

t = -v0y / a

t = -106.1 m/s / (-9.81 m/s^2)

t = 10.8 s

Now we can calculate the maximum height using the vertical component of the velocity and the time it takes to reach it:

y = v0y * t + 1/2 * a * t^2

y = 106.1 m/s * 10.8 s + 1/2 * (-9.81 m/s^2) * (10.8 s)^2

y = 293.3 m = 0.293 km

Therefore, the answer is C) 0.57 km (rounded to two decimal places).

You Shoot an Arrow with a Mass of 0