Siblings Alice and Bob saved their money all summer to buy a water balloon launcher, and they are eager to take it for a test run. Younger brother Bob thinks he's a pretty fast runner with a top speed of 5 m/s. He poses the following challenge to his sister: "I'll stand 20 m from you and I'll start running away as soon as you launch a water balloon. See if you can hit me!" Unfortunately for Bob, Alice is a physics 8A ace and knows exactly what needs to be done to soak her brother. (a) Set the origin of your coordinate system at Alice's position with Bob starting along the positive x-axis (and running along the x-axis). Assuming Bob runs at a constant velocity, what is Bob's trajectory rB(t)? (b) Suppose the water balloon launcher is limited to only firing at an angle of 7/4. In terms of the unknown initial launch speed v, what is the trajectory of the water balloon rwB(t)? (c) What speed v should Alice launch with to ensure a direct hit?

Siblings Alice and Bob saved their money all summer to buy a water balloon launcher, and they are eager to take it for a test run. Younger brother Bob thinks he's a pretty fast runner with a top speed of 5 m/s. He poses the following challenge to his sister: "I'll stand 20 m from you and I'll start running away as soon as you launch a water balloon. See if you can hit me!" Unfortunately for Bob, Alice is a physics 8A ace and knows exactly what needs to be done to soak her brother. (a) Set the origin of your coordinate system at Alice's position with Bob starting along the positive x-axis (and running along the x-axis). Assuming Bob runs at a constant velocity, what is Bob's trajectory rB(t)? (b) Suppose the water balloon launcher is limited to only firing at an angle of 7/4. In terms of the unknown initial launch speed v, what is the trajectory of the water balloon rwB(t)? (c) What speed v should Alice launch with to ensure a direct hit?