If emily throws the ball at an angle of 30∘ below the horizontal with a speed of 14m/s, how far from the base of the dorm should allison stand to catch the ball? assume the vertical distance between where emily releases the ball and allison catches it is 4.0m.

Emily throws the ball at 30 degree below the horizontal

so here the speed is 14 m/s and hence we will find its horizontal and vertical components

vertical distance between them

now we will use kinematics in order to find the time taken by the ball to reach at Allison

here acceleration is due to gravity

now we will have

now solving above quadratic equation we have

now in order to find the horizontal distance where ball will fall is given as

here it shows that horizontal motion is uniform motion and it is not accelerated so we can use distance = speed * time

so the distance at which Allison is standing to catch the ball will be 5.33 m

The horizontal distance from the base of the dorm Allison should stand in order to catch the ball is 5.3 m.

The given parameters;

The time of motion of the ball from the given height is calculated as follows;

The horizontal distance traveled by the ball is calculated as follows;

Thus, the horizontal distance from the base of the dorm Allison should stand in order to catch the ball is 5.3 m.

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