Jonathan S. answered • 02/20/23
Experienced Math Educator and Former Google Software Engineer
a) To find the initial vertical velocity of the soccer ball, we can use the equation v = v0 + at, where v is the final velocity, v0 is the initial velocity, a is the acceleration, and t is the time. Since the ball starts on the ground, we can assume that the initial vertical velocity is 0. The only force acting on the ball in the vertical direction is gravity, which causes it to accelerate downwards at a rate of 9.8 m/s^2. Therefore, the vertical component of the initial velocity is:
v0_y = 20 sin(30) = 10 m/s
b) At peak height, the ball will stop momentarily before it starts to fall back down. Therefore, its vertical velocity at peak height will also be 0 m/s.
c) The initial horizontal velocity of the soccer ball is given by:
v0_x = 20 cos(30) = 17.32 m/s
d) To find how long it will take the soccer ball to reach peak height, we can use the equation v = v0 + at again. Since the final velocity at peak height is 0 m/s, we can use this equation to find the time it takes for the vertical velocity to become 0:
0 = 10 - 9.8t
t = 10/9.8 = 1.02 s
Therefore, it takes 1.02 seconds for the ball to reach peak height.
e) To find how far the ball will travel before hitting the ground, we can use the equation d = v0t + 0.5at^2, where d is the distance travelled, v0 is the initial velocity, a is the acceleration, and t is the time. Since the ball starts and lands on the ground, we only need to find the horizontal distance it travels:
d = 17.32 * 2 * 1.02 = 35.27 m
Therefore, the ball will travel 35.27 meters before hitting the ground.
