23. A friend of yours has a one-story house with a pool in the backyard. Someone gets the bright idea to jump from the roof of the house into the deep end of the pool S tho roof of the house is 16 ft tall and the horizontal distance between the edge a. of the house and the pool is 10 ft, what would the jumper's minimum velocity need to be to land in the pool? Let's assume your friend can jump with an initial horizontal velocity of 15 ft/ s. What is their total velocity when they hit the water? (hint: determine both the x and y b. velocity components, find the resultant)

6. man stands on the roof of a 50 m tall building and throws a ball with a speed of 25 m/s at 40° above the horizontal. If we ignore the air resistance; a. Find the vertical and horizontal components of the ball's initial velocity. b. Find the maximum height above the ground that the ball reaches. c. Find the ball velocity (in unit vector nutation) just before it strikes the ground. d. At what horizontal distance from the edge of the building does the ball strikes the ground? e. What is the vertical acceleration of the ball at the maximum height? a. Vox 19.15 m/s Voy 16.07 m/s b. y = 50+ 13.18 = 63.18 m e. c. Vx = Vox = 19.15 m/s v=vxî + vyĵ = 19.15î — 35.18ĵ d. x = 100.16 m ay = -9.8 m/s² Vy = -35.18 m S 0000000000 00 DO 00 00 vo 40° 50 m

To celebrate the start of October, you want to win a pumpkincatapult contest, which requires you to build a catapult and launcha pumpkin from it. You build your catapult so that it releases thepumpkin when the catapult arm is exactly vertical, as shown inthe picture. a.Draw a picture and make a list of known and unknownquantities for the scenario b.Suppose the catapult arm has a length of R = 3 m and the pumpkin undergoes uniform circular motion with an acceleration of a = 75 m/s^2 before it is launched. What is the speed of the pumpkin at the moment it is launched?

B. Answer the following problems. Show your complete solutions. 1. If a stone is thrown vertically upward from the surface of the moon with a velocity of 10 meters per second (m/s), its height (in m) after t seconds (s) is h = 10t - 0.83F. a. What is the velocity of the stone after 3 s? b. What is the velocity of the stone if it has risen by 25 m? 2. A spherical balloon is being inflated. Find the rate of increase if the surface area (S = 4tr²) with respect to the radius r are the following: a. 0.3 m b. 0.61 m C. 0.91 m Differentiation and Integration