Problem 5 (Physics refresher) When air resistance is negligible, a projectile near the surface of the earth is subjected only to the force of gravity. In that case, Newton's second

law tells us that the projectile's acceleration is constant and downward. Denote by(r, y) the position of the projectile, such that y is the vertical distance from the ground,and r is the distance along the ground in the direction of motion. Then the projectile's acceleration (a,y) has the following components: a_{x} \equiv \frac{d^{2} x}{d t^{2}}=0, \quad a_{y} \equiv \frac{d^{2} y}{d t^{2}}=-g where t is time, and g is the local acceleration due to gravity near the earth's surface (in SI units, g 9.8 m/s). )(6 points) Starting from (2), integrate to find the projectile's velocity components r(t) = dr/dt and e,(t) dy/dt as functions of time t, subject to the initial conditions v, (0) , and r,(0)= l0. Leave your answer in terms of g. ) (6 points) Integrate again to find the projectile's position components r(t) and y(t) as functions of time t, subject to the initial conditions r(0) ro and y(0) leave your answer in terms of g.= . )Suppose you throw a baseball of mass 0.145 kg from an initial height of yo 1 m above the ground at a speed of 40.2 m/s (90 mph) at an angle of 20° from the horizontal.Using your answers to parts (a) and (b) above, answer the following questions: How long does it take for the ball to hit the ground? How far does the ball travel horizontally during that time? What is the maximum height of the ball above the ground?