Question

A student observes that the motion of a weight oscillating up and down on a spring can be modeled by the following equation, where h is the weight's height above the ground, in meters, and t is the time, in seconds.
h(t)=0.5 x sin(πt+π/2)+1

On the graph, plot the points where height, h(t), is at a maximum.

Answer 1

Answer:

the height will be maximum at 1.5

Step-by-step explanation:

We have been given the function:

$h(t)=0.5\cdot sin(\pi t+\frac{\pi}{2})+1$

Height depends on $(sin(\pi t+\frac{\pi}{2})$

$(sin(\pi t+\frac{\pi}{2})$

This will be maximum when value of its is 1

And value will be 1 when t=0.

So, substitute the value of t=0 in given function:

$h(0)=0.5\cdot sin(\pi 0+\frac{\pi}{2})+1$

$h(0)=0.5\cdot sin(\frac{\pi}{2})+1$

$\Rightarrow h(0)=0.5(1)+1$

$h(t)=1.5$

Hence, the height will be maximum at 1.5