Question

The height of a moving object is given by h(t) = h0 a sin kt 6 where a, k and h0 are positive constants. answer the following questions. your answers may include some, none, or all of the unknown constants. you do not need units. (a) find the velocity of the object at the instant when t = 4 seconds.

Answer 1

The velocity of the object at 4 seconds is given by v(4) = a k cos(4k), where 'a' and 'k' are constants from the original height function h(t) = h0 + a sin(kt) - 6.

Step-by-step explanation:

To find the velocity of the object at the instant when t = 4 seconds, we first need to differentiate the height function h(t) with respect to time t to get the velocity function v(t). The given height function is h(t) = h0 + a sin(kt) - 6. We differentiate each term separately:

• The derivative of a constant h0 is 0.
• The derivative of a sin(kt) with respect to t is a k cos(kt) by the chain rule.
• The derivative of a constant -6 is 0.

So the velocity function v(t) is given by:

v(t) = a k cos(kt)

To find the velocity at t = 4 seconds, we substitute t with 4:

v(4) = a k cos(4k)

Without specific values for a and k, this is as far as we can simplify.