a rock is dropped from a 400 ft building. the equation for height as a function of time is h(t)=-16t² +…

a rock is dropped from a 400 ft building. the equation for height as a function of time is h(t)=-16t² + initial height, where t is time in seconds and h(t) is height in ft. how long will it take for the rock to hit the ground? 0=-16t² + 400 solve for t. t = ±5 t = ±80

a rock is dropped from a 400 ft building. the equation for height as a function of time is h(t)=-16t² + initial height, where t is time in seconds and h(t) is height in ft. how long will it take for the rock to hit the ground? 0=-16t² + 400 solve for t. t = ±5 t = ±80

Answer

Explanation:

Step1: Isolate the variable term

Starting with $0=-16t^{2}+400$, we first move $16t^{2}$ to the left - hand side. So, $16t^{2}=400$.

Step2: Solve for $t^{2}$

Divide both sides of the equation $16t^{2}=400$ by 16. We get $t^{2}=\frac{400}{16}=25$.

Step3: Find the value of $t$

Take the square - root of both sides. Since $t^{2}=25$, then $t = \pm\sqrt{25}=\pm5$. But time cannot be negative in this context (we are talking about the time it takes for the rock to fall), so we discard the negative value.

Answer:

$t = 5$ seconds