A soccer ball is kicked with the initial speed of 10.7m/s . After 0.780s it is at its highest point. What was its initial direction of motion?
Well, it sounds like this soccer ball was definitely aiming for the sky! I guess you could say its initial direction of motion was up, up, and away!
To determine the initial direction of motion of the soccer ball, we need to consider the motion and trajectory of the ball at its highest point.
At the highest point of the soccer ball's motion, its vertical velocity is momentarily zero. This means that the upward motion of the ball has stopped, and it will start moving downward due to the force of gravity.
Since the ball is moving downward at its highest point, we can conclude that its initial direction of motion was upwards.
To find the initial direction of motion of the soccer ball, we need to analyze the vertical motion of the ball.
Given:
Initial speed (u) = 10.7 m/s
Time to reach the highest point (t) = 0.780 s
When the soccer ball reaches its highest point, its vertical velocity (v) will be zero. This is because at the highest point of its trajectory, the ball momentarily stops moving upwards before starting to fall back down due to the force of gravity.
Using the kinematic equation for vertical motion:
v = u + gt
where:
v = final velocity (0 m/s)
u = initial velocity (10.7 m/s)
g = acceleration due to gravity (-9.8 m/s^2, considering upwards as positive)
0 = 10.7 + (-9.8)(0.780)
-10.7 = -7.644
From the equation, we can see that the initial velocity and acceleration have opposite signs, causing the velocity to decrease until it reaches zero at the highest point.
Therefore, based on this calculation, the soccer ball was initially moving in the upward direction.
Vy = vo sinθ - gt
0 = 10.7 sinθ - (9.81 x 0.780)
sinθ = gt / Vo
(9.81 x 0.780) / 10.7 = 0.7151
θ = sin^-1 (0.7151) = 45.65 degrees
v = Vi - g t
v = 0 at top
0 = Vi - 9.81(.78)
Vi = 7.65 m/s initial speed up
sin T = 7.65/10.7
T = 45.65 degrees up from horizontal