A wagon with a width of 2.4 m, moving at a speed of 15 m per second, was shot through by a bullet
perpendicular to the movement of the wagon. The distance between the two bullet holes in the
wagon’s walls is 6 cm. What is the speed of the bullet?
How long does it take the wagon to move .06 meters?
.06 = 15 t
t = .004 seconds
So
the bullet moved 2.4 meters in .004 seconds
v = 2.4/.006 = 400 m/s
2.4/.004 = 600 m/s
The bullet moved 2.4 meters in the same time the cart moved .06 meters
so
bullet spped = wagon speed *(2.4/.06)
= 15 * 2.4/.06
= 600 m/s
To find the speed of the bullet, we can use the concept of relative velocity. Relative velocity describes the motion of one object with respect to another object. In this case, we'll consider the wagon as the reference point and calculate the relative velocity of the bullet.
Given:
Width of the wagon = 2.4 m
Speed of the wagon = 15 m/s
Distance between the bullet holes in the wagon's walls = 6 cm = 0.06 m
To start, let's assume that the bullet traveled straight through the wagon without any deflection or change in speed. Therefore, the distance the bullet traveled inside the wagon is equal to the width of the wagon.
Distance the bullet traveled inside the wagon = Width of the wagon = 2.4 m
We know that distance = speed × time. Since the bullet traveled straight through the wagon perpendicular to its motion, the time it took for the bullet to travel through the wagon is the same as the time it took for the wagon to move its width.
Time taken for the bullet to travel through the wagon = Time taken for the wagon to move its width
To find the time taken for the wagon to move its width, we can use the formula:
Time = Distance / Speed
Time taken for the wagon to move its width = Width of the wagon / Speed of the wagon
= 2.4 m / 15 m/s
= 0.16 s
Therefore, the time taken for the bullet to travel through the wagon is also 0.16 seconds.
Now, we can calculate the speed of the bullet using the formula:
Speed = Distance / Time
Speed of the bullet = Distance the bullet traveled inside the wagon / Time taken for the bullet to travel through the wagon
= 2.4 m / 0.16 s
= 15 m/s
Hence, the speed of the bullet is 15 m/s.