Final answer:
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.