Projectile motion: Let's suppose you throw a ball straight up with an initial speed of 50 feet per second from a height of feet.
a) Find the equation that describes the motion as a function of time.
My answer was x = 0 and y=-16t^2+50t+6
b) How long is the ball in the air?
This is the part I need help on. Can I put the y equation into my graphing calculator to solve for t?
you can, but it is not necessary.
when it returns to ground, y=0
0=-16t^2+50t+6
16t^2-50t-6=0
using the quadratic equation...
t= (50+-sqrt(2500+384)/32
t=(50+-sqrt 53.7)/32=103.7/32=3.24sec
Your graphing calc may have a subrouting to solve quadratic equations, many do.
check my work.
Yes, you can indeed use your graphing calculator to solve for the time when the ball is in the air. To do this, you need to solve the equation -16t^2 + 50t + 6 = 0 for t.
Here's how you can input this equation into your graphing calculator to solve for t:
1. Turn on your graphing calculator and go to the equation-solving feature. This is usually denoted by a button or option with a "solve" or "zero" symbol.
2. Input the equation -16t^2 + 50t + 6 = 0 into the equation-solving function of your graphing calculator.
3. Once you have inputted the equation, your graphing calculator will solve for all the values of t that satisfy the equation. Typically, the calculator will give you multiple solutions, since there could be more than one intersection point between the projectile's path and the y-axis.
4. Look for the positive values of t, as these represent the time when the ball is in the air. Ignore any negative solutions, as they indicate time values prior to the ball being thrown.
5. The positive values of t you obtain from your graphing calculator represent the time (or times) when the ball is in the air.
By using this method, you can determine how long the ball is in the air based on the given equation of motion.