Question

a toy rocket is launched from the top of a building 50 ft. tall at an initial velocity of 90 ft per second. Let t represent the amount of time elapsed after the launch. Solve.

the answer is y= -16x2 + 90x + 50
How did the get the -16x squared??

Answer 1

Well... The general form of the equation that gives the height (h) of an object propelled upwards, as a function of time (t) is: {{{h(t) = -(1/2)gt^2+v[0]t+h[0]}}} where: h is the height in feet, t is the time in seconds, g is the acceleration due to gravity ({{{g = 32 ft/sec^2)}}}, {{{v[0]}}} is the initial velocity of the object, and {{{h[0]}}} is the initial height of the object. If you wanted to graph such an equation (it would be a parabola opening downward), it would be written as: {{{y = -16t^2+v[0]t+h[0]}}} The x in your equation is a replacement variable for the time, t. The first term {{{-16t^2}}} is negative because of the downward effect of gravity on the object. Just for fun, let's see what your equation would look like when graphed: {{{graph(600,400,-5,8,-5,200,-16x^2+90x+50)}}}