Question

1. If two objects at a certain height are thrown horizontally at the same time with opposite speeds of 50 m / s and 18 m / s in opposite directions, how many seconds later will the angle between the velocity vectors of these objects be 90
Degree?

Answer 1

1. Let us say that the resultant velocity is v and the horizontal and vertical velocities are vx and vy respectively. Now we can calculate the angle with respect to the vertical as,

The horizontal velocities of both the objects will be equal at 50 m/s and 18 m/s. Only the vertical velocity will change. The magnitude of vertical velocity can be given as,

For the first object thrown towards left at 50 m/s the angle with respect to vertical is given as,

For the second object with is thrown towards right at 18 m/s the angle with respect to the vertical is given as,

The sum of these angles should be equal to 90 degrees. Hence we can write,

Applying tan on both sides and applying trigonometric identity we can write,

the value of tan(90) is infinity, this implies that the denominator on the right hand side is 0. Hence we can write,

Therefore the angle between the velocity vectors of these two objects will be 90 at time t = 2.47 seconds.