During football practice, a football is kicked with a speed of 22 m/s at an angle of 60.0° relative to the positive x direction. at that instant, an observer rides past the football in a car that moves with a constant speed of 11 m/s in the positive x direction. determine the initial velocity of the ball relative to the observer in the car.

The speed of 22 m/s is not in the x-direction, but in the direction it is kicked. To determine the speed in the direction the ball is kicked, we can set up a right triangle where the hypotenuse is 22 m/s, the leg length on the ground is x, the leg length in the air is y, and the angle between the hypotenuse and the ground is 60 degrees. In this case the remaining angle is 30 degrees since the sum of the angle degrees of a triangle is 180 degrees. In a 30-60-90 triangle, the hypotenuse is twice the length of the leg meeting the hypotenuse at the 60 degree angle. Thus x = 11 and the football's speed in the positive x direction is 11 m/s. The car moves in the same direction as the football at the same speed, 11 m/s. Therefore, to the driver, the football is not moving at all in the x-direction. So the relative initial speed is 0 m/s in the x direction. However, the ball is still moving upward relative to the car. The upward velocity is y, which using the Pythagorean Theorem equals 11sqrt (3). Therefore the initial velocity of the ball relative to the car is 0 m/s in the positive x direction and 11sqrt (3) in the positive y direction.