Answer:
Step-by-step explanation:
Let us examine all options:
(a)
Lets verify for t = 0:
h(t = 0) = 7
This isn't allowable as 14 cm is the lower limit for the ball's motion.
This is rejected.
(b)
Let's verify for t = 0:
h(t = 0) = 14
Since at t = 0 sec, the ball is at its minimum, after 2 seconds, it should be at its maximum.
But h(t = 2) = 14, which doesn't satisfy the condition.
Hence, this is rejected.
(c)
Now, let's see at what time instance, the ball is at minimum in this case:
h(t) = 14 = 18sin(πt) + 32
∴ sin(πt) = -1
∴ πt = 3π/2
∴ t = 3/2 seconds
Hence, after 2 seconds, i.e. at 3.5 seconds, the ball should be at its maximum.
h(t = 3.5) = 18sin(3.5π) + 32 = -18 + 32 = 14, which doesn't satisfy the condition.
Hence, this is rejected,
(d)
Now, let's see at what time instance, the ball is at minimum in this case:
h(t) = 14 = 18sin(πt/2) + 32
∴ sin(πt/2) = -1
∴ πt/2 = 3π/2
∴ t = 3 seconds
Hence, after 2 seconds, i.e. at 5 seconds, the ball should be at its maximum.
h(t = 5) = 18sin(5π/2) + 32 = 18 + 32 = 50, which satisfies the condition.
Hence, option (D) is the right answer
