Questions: If an object is projected upward with an initial velocity of 123 ft per sec, its height h after t seconds is h=-16t^2+123t. Find the height of the object after 4 seconds. The height of the object after 4 seconds is ft.

Solution Steps

We are given the height function of an object projected upward: $$h(t) = -16t^2 + 123t$$ We need to find the height of the object after 4 seconds.

Substitute $t = 4$ into the height function: $$h(4) = -16(4)^2 + 123(4)$$

First, calculate $4^2$: $$4^2 = 16$$

Now substitute back into the equation: $$h(4) = -16(16) + 123(4)$$

Calculate each term: $$-16 \times 16 = -256$$ $$123 \times 4 = 492$$

Add the results: $$h(4) = -256 + 492 = 236$$

Final Answer