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

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

option a.

step-by-step explanation:

if you look closely at the graph, we can notice that the function is not defined at two different points.

if you look at functions b and c, you will notice that both functions are not defined at just one point. the function b is not defined at x= -5/2 and function c is not defined at x=-5. both options are discarded, given that our function should not be defined at two fiferent points.

now, if you look closely at the graph you will notice that the function sketched is not defined at x=5 and x=-2.

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