Consider the diagram below. The blue path represents the trajectory of a projectile dropped from rest from the top of the path. (Each ball location represents the location after a 1-second interval of time.) The red path represents the trajectory of the same ball thrown horizontally in the absence of gravity. Construct a third path accurately showing the trajectory of a projectile launched with the same horizontal speed as the red ball. Show the location during the first four seconds of motion. Finally, the (x, y) coordinate position of location 1 is (0 m, -5 m) and the (x, y) coordinate position of location 2 is (15 m, 0 m). Determine the (x, y) coordinate positions of the four locations in your trajectory. (Assume g ~10 m/s/s.)

Water leaves a fireman’s hose (held near the ground) with an initial velocity v0 = 11.5 m/s at an angle θ = 30.5° above horizontal. Assume the water acts as a projectile that moves without air resistance. Use a Cartesian coordinate system with the origin at the hose nozzle position, as shown. 1). Using v0, θ, and g, write an expression for the time, tmax, the water travels to reach its maximum vertical height.  2)

Consider a projectile being launched with an initial speed of 43 m/s at a variety of initial angles. Refer to the figure. What is the range, in meters, of the projectile if it is launched at an angle of θ1 = 79.7°?  What is the range, in meters, of the projectile if it is launched at an angle of θ2 = 40.5°?  What is the range, in meters, of the projectile if it is launched at an angle of θ3 = 90 − 79.7°, the complement of θ1?

The figure below shows the motion diagram of two balls. The time interval between images is 0.036 s. Each ball starts at point i. The ball on the left is released and falls straight down. At the same time, the ball on the right is launched horizontally and follows the path shown. (Express your answers in vector form. Use exactly 9.81 for the acceleration due to gravity. Indicate the direction with the sign of your answer.) y (cm) 90 80 B 70D •D E 60 •F 50FG 40H 301 20 •J 10 K K 50 x (cm) 10 20 30 40 60 (a) Write the velocity and acceleration of each ball as a function of time. (Use the following as necessary: t and vy for the intial velocity in the x direction of the ball on the right. Do not substitute numerical values for t and vx; use those variables only.) for the ball on the left v = m/s a = m/s2 for the ball on the right v = m/s a = m/s2