Question

An iron ball is bobbing up and down on the end of a spring. The maximum height of the ball is 50 centimeters and its minimum height is 14 centimeters. It takes the ball 2 seconds to go from its maximum height to its minimum height.
Which model best represents the height, h, of the ball after t seconds?


h(t)=25sin(πt)+7

h(t)=50sin(πt / 2)+14

h(t)=18sin(πt)+32

h(t)=18sin(πt /2)+32

Answer 1

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