The projectile motion equation is s(t)=-16t^2+vt+h where s(t) represents the distance or height of an object...

The projectile motion equation is s(t)=-16t^2+vt+h where s(t) represents the distance or height of an object at time t, v represents the initial speed of the object in ft/s, and h is the initial height of the object, measured in feet.

If an object is starting at rest, then v=0 (such as for a penny being dropped from a building). If the object is starting from the ground, h=0. The baseball or cannonball situations, each have an initial velocity. For example, the initial velocity of the baseball is based on the speed at which the ball comes at you (the speed of the pitch).

Come up with a situation that you can model with this equation. Describe the situation and tell us what v and h are. Fill in the values so that you have a quadratic equation. If you do research to find initial velocities, include the links to the websites where you found that information. If you would like to make up your own numbers as well, you can (be creative)!

Once you have your equation, find the maximum height as well as the time it takes to reach that maximum. Then use your equation to find when the object hits the ground (i.e. the x-intercepts).

Finally, use those three points as well as the initial height to sketch a graph. You can take a photo of it and include the image or use an online graphing calculator and take a screenshot if that is easier.

Solutions

Expert Solution

Here are the steps required for Solving Projectile Motion Problems:

Step 1: Set the given equation equal to the appropriate height.

Step 2: Solve the equation found in step 1 by setting the equation equal to zero and factoring the equation.

Step 3: Based on the problem, determine which answer or answers are correct. Do not forget to include the units in your final answer.

Example:

ball is thrown straight up from the top of a 128 foot tall building with an initial speed of 32 feet per second. The height of the ball as a function of time can be modeled by the function h(t) = –16t² + 32t + 128. How long will it take for the ball to hit the ground?

Step 1: Set the given equation equal to the appropriate height. In this case, we set the equation equal to zero because the height of the ground is zero.
Step 2: Solve the equation found in step 1 by setting the equation equal to zero and factoring the equation.
Step 3: Based on the problem, determine which answer or answers are correct. Do not forget to include the units in your final answer. In this case, there is only one positive answer which makes sense because the ball will only strike the ground once.

genius_generous answered 1 year ago

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