Problema Solution
At a basketball game, members of the Spirit Club use a t-shirt cannon to launch team t-shirts to spectators in the stands. The equation below describes the height, h, of the t-shirt, t seconds after it is shot from the cannon c feet above the ground, at an initial velocity of v.
h = -16t^2 + vt + c
Solve the equation for initial velocity, v.
The cannon launched a t-shirt from an initial height of 5 feet. After 3 seconds the shirt has reached a height of 131 feet. Use your equation from #1 to find the initial velocity of the t-shirt. Show your work.
What does the equation from #1 tell you about the value of the velocity, v, when t = 0? Explain.
Answer provided by our tutors
This problem should be solved using Algebrator. You can solve for a specific variable by entering the equation into a new worksheet, pressing "Solve All" and then choosing the variable to solve for (so simply choose 'v').
The equation, once solved for 'v', now expresses a function dependent on 'h', 't' and 'c'. You can replace the variables with their numeric values (131, 3 and 5, respectively) and solve for 'v', the initial velocity.
You will find that the equation initially solved for (v=...) contains 't' as a denominator and therefore the equation is undefined when t=0 and can not tell you anything regarding velocity at t=0.
Trial versions of Algebrator may be downloaded from these links:
Windows: http://www.softmath.com/tr/alg51win-tr-en.exe