1. Wile E. Coyote launches a water balloon from the top of a 140-foot tall building with an initial velocity of 50 ft/s. Assuming an acceleration due to gravity of –32 ft/s² and no wind resistance, (a) Solve an initial value problem to find v(t), the velocity of the water balloon at time t. (b) Solve an initial value problem to find s(t), the height of the water balloon at time t. (c) At what time does the water balloon reach its highest point? How high is it at that point? (d) The Road Runner, who is 2 feet tall, is standing underneath the falling water balloon. If he doesn't move out of the way in time, how fast will the water balloon be going when it hits him on the top of the head?

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.