Question

A tether ball is attached to a vertical pole with a cord of length L. Assume the size of the ball itself is negligible. When struck by a bear, the ball moves in a horizontal circle at a constant speed v, and with the cord making an angle of 8 with the vertical. If the cord length is L = 1.5 m, and if the bear can hit the ball at a speed of v = 13 m s-¹, find the angle of the cord with vertical that will allow the ball to travel around a full circle in a time of 0.50 s and surprise the bear from behind.​

Answer 1

The length of the cord needs to be approximately 1.03 meters in order to allow the ball to travel around a full circle in a time of 0.50 s and surprise the bear from behind.

Step-by-step explanation:

To find the angle of the cord with vertical that will allow the ball to travel around a full circle in a time of 0.50 s and surprise the bear from behind, we can use the concept of centripetal acceleration.

The centripetal acceleration is given by the equation a = (v^2)/r, where v is the speed and r is the radius of the circle. In this case, the radius is equal to the length of the cord, L.

Given that the speed v is 13 m/s and the time for a full circle is 0.50 s, we can use the relation v = 2πr/t, where r is the radius of the circle and t is the time.

Substituting the values, we have 13 = 2π(L)/(0.50).

Simplifying the equation, we can find the value of L: L = (13)(0.50)/(2π) = 1.03 m.

Therefore, the length of the cord needs to be approximately 1.03 meters in order to allow the ball to travel around a full circle in a time of 0.50 s and surprise the bear from behind.