Final answer:
To calculate the time it takes for a ball to reach the wall, one must use the horizontal component of the ball's initial velocity to find the time by dividing the horizontal distance from the wall by the horizontal velocity. It's found to be approximately 0.385 seconds.
Step-by-step explanation:
The student has asked how to calculate the time it takes for a ball to reach a wall when the ball is kicked from ground level 5 m from the wall with an initial speed of 15 m/s, directed 30 degrees above the horizontal. To solve this problem, we'll use the horizontal component of the ball's velocity. Since there is no air resistance and we're only considering the horizontal motion for the time calculation, we can ignore the vertical component.
First, we need to calculate the horizontal velocity component (vx) using the initial speed and the angle given:
vx = v * cos(θ)
Substituting the given values:
vx = 15 m/s * cos(30°)
vx = 15 m/s * (√3/2)
vx = 12.99 m/s (approx)
Now, we calculate the time (t) using the horizontal distance (d) and horizontal velocity (vx):
t = d / vx
Substituting the known values:
t = 5 m / 12.99 m/s
t = 0.385 s (approx)
So the ball will take approximately 0.385 seconds to reach the wall.