7.1

The minimum distance from home plate to the homerun fence at center field at any MLB Ball Park must be 400 ft away and the fence must be 8ft tall. A baseball hit at the statistics given above will not produce a home run. If the exit velocity is maintained at vo = 125 /s, use a graphing utility to approximate the minimum exit angle 0 that will produce a home run. Record the new parametric equations below. d. If the exit velocity is maintained at vo = 125 /s, use a graphing utility to determine the exit angle that will maximize the horizontal distance of a baseball.3. (Physics: Projectile Motion) In your first semester physics course, you will learn the subject of Kinematics which deals with Projectile Motion. For this problem we'll be looking at the individual horizontal and vertical components of an object. The parametric equations for the motion of a baseball hit at an angle 0 is given by: x(t) = (vo cos(0))t y(t) - h + (vo sin(0))t - 5gtz Where vo is the exit velocity, 0 is the exit angle, h is the initial vertical height, and g is the acceleration due to gravity. a. Suppose a baseball is hit 3ft above the ground, with an exit angle of 20', and an exit velocity of 125 / 7. Record the parametric equations for the baseball below. Assume g = 32 // 22. (RL Circuits Continued) In Section 4.2, we did the slope field of a Resistor-Inductor Circuit that's present in early versions of a home's doorbell. Resistor (R) In an RL circuit, an inductor is an electrical component that opposes the Battery (E) change in electrical current. That is, an inductor slows down the passing of a current through a circuit. The equation that describes the passing of Inductor (L) current through the circuit is given by the first-order differential equation 4 d F Switch L . + R . I = E + 121 = 60 dt it Where I is the inductance measured in Henrys (H), I is the current measured in Amps (A), R is the resistance measured in ohms (0), E is the battery measured in volts (V), measured over t seconds. a. Suppose a 4H inductor, a 120 resistor, a 60V battery, and a switch is placed into the circuit pictured above. Derive, and solve, the first order separable differential equation that describes the current I over t seconds that goes through the initial condition (0,1). Your answer should be a function I (t)b. Use your answer to find the current through the circuit at 3 seconds