Calculating the Velocity of an Arrow Shot from a Crossbow
How can we calculate the velocity of an arrow just as it emerges from a crossbow?
Calculating the Velocity of an Arrow:
Explanation:
The problem involves determining the initial velocity of an arrow shot from a crossbow. Since the arrow strikes 10.0 cm below the bull's eye, we can assume that it follows a parabolic trajectory. By utilizing the concept of projectile motion, we can calculate the initial velocity. The formula to use is y = v0t - (1/2)gt^2, where y is the vertical displacement, v0 is the initial velocity, t is the time of flight, and g is the acceleration due to gravity.
We know that the vertical displacement is -0.10 m (10.0 cm). The problem states that the crossbow is aimed horizontally, which means there is no vertical velocity component (vy = 0). Therefore, we can rewrite the equation as y = (1/2)gt^2. The distance to the target is 50.0 m, and since the crossbow is aimed horizontally, the horizontal displacement (x) equals 50.0 m.
The horizontal velocity (vx) can be calculated using vx = x/t. We can then use the equation x = vxt to find the time of flight (t) for the arrow. Once we have the value of t, we can substitute it into the equation y = (1/2)gt^2 to find the value of g. Finally, we can find the initial velocity (v0) by using vy = gt.