NASA launches a rocket at t=0 seconds. Its height, in meters above sea-level, as a function of time is given by h(t)=−4.9t2+223t+241.Assuming that the rocket will splash down into the ocean, at what time does splashdown occur?The rocket splashes down after □ seconds.How high above sea-level does the rocket get at its peak?The rocket peaks at □ meters above sea-level.
Q. NASA launches a rocket at t=0 seconds. Its height, in meters above sea-level, as a function of time is given by h(t)=−4.9t2+223t+241.Assuming that the rocket will splash down into the ocean, at what time does splashdown occur?The rocket splashes down after □ seconds.How high above sea-level does the rocket get at its peak?The rocket peaks at □ meters above sea-level.
Identify Equation: Identify the equation for the height of the rocket as a function of time: h(t)=−4.9t2+223t+241. To find the splashdown time, solve for t when h(t)=0.
Calculate Discriminant and Roots: Calculate the discriminant b2−4ac and then the roots.
Calculate Positive Root: Calculate the positive root since time cannot be negative.
Find Peak Height Time: To find the peak height, use the vertex formula t=−2ab for the time at which the peak occurs.
Substitute for Peak Height: Substitute tpeak back into the height equation to find the peak height.
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