Final answer:
The ball projected upward with an initial speed of about 40 m/s will be moving downward at a speed of approximately 30 m/s around 3 seconds after projection, making option 'd' the correct answer.
Step-by-step explanation:
The student's question pertains to a classic problem in physics, specifically kinematics, dealing with the motion of a projectile under the influence of gravity, assuming no air resistance. We can apply the kinematic equations for uniformly accelerated motion to solve this problem.
Given that the initial vertical speed is 40 m/s and gravity will decelerate the ball at a rate of approximately 9.8 m/s2, we want to find out when the ball will be moving downward at approximately 30 m/s. The formula for final velocity v is:
v = u + at
Where:
- v is the final velocity,
- u is the initial velocity,
- a is the acceleration, and
- t is the time.
As the ball reaches its peak and starts to fall down, the initial velocity will be 0 m/s at the highest point, and the acceleration due to gravity is -9.8 m/s2 (the negative sign indicates the direction of acceleration is opposite to the initial upward motion). Therefore, the time 't' when the ball would have a downward speed of 30 m/s can be calculated using the formula:
30 = 0 - (9.8)t
t = 30 / 9.8 ≈ 3.06 seconds
Therefore, the correct answer is 'd. 3 seconds after projection' as this is the closest time to our calculation where the ball would have approximately 30 m/s downward speed.