A home run is hit in such a way that the baseball just clears a wall 14.0 m high

Question

A home run is hit in such a way that the baseball just clears a wall 14.0 m high, located 124 m from home plate. The ball is hit at an angle of 37.0° to the horizontal, and air resistance is negligible. (Assume that the ball is hit at a height of 1.0 m above the ground.)

(a) Find the initial speed of the ball. m/s

(b) Find the time it takes the ball to reach the wall. s

(c) Find the velocity components of the ball when it reaches the wall. x-component m/s y-component m/s Find the speed of the ball when it reaches the wall. m/s

2. An astronaut orbiting the Earth is preparing to dock with a Westar VI satellite. The satellite is in a circular orbit 800 km above the Earth's surface, where the free-fall acceleration is 8.13 m/s2. Take the radius of the Earth as 6400 km.

a. Determine the speed of the satellite. m/s

b. Determine the time interval required to complete one orbit around the Earth, which is the period of the satellite. min

3. We found the centripetal acceleration of the Earth as it revolves around the Sun. Compute the centripetal acceleration of a point on the surface of the Earth at the equator caused by the rotation of the Earth about its axis. (The radius of the Earth is 6,371 km.) m/s2

Please help, thank you

Explanation / Answer

vertical distacne travelled is 14-1 = 13 m

So using kinematic equations

y = (Vo*sin(37))-(0.5*g*t^2)

13 = (Vo*sin(37)*t) - (0.5*9.81*t^2)

Horizontal distance travelled is

x = Vo*cos(37)*t

124 = Vo*cos(37)*t

t = 124/(Vo*cos(37))

So

13 = (Vo*sin(37)*124/(Vo*cos(37)) - (0.5*9.8*(124/(Vo*cos(37))^2)

13 = 124*tan(37) - (4.9*(124/(Vo*cos(37))^2))

13 = 93.44 - (4.9*(124/(Vo*cos(37))^2))

(4.9*(124/(Vo*cos(37))^2)) = 93.44-13 = 80.44

Vo^2*cos^2(37) = 4.9*124^2/80.44 = 936.62

Vo^2 = 936.62/cos^2(37) = 1468.5

Vo = 38.4 m/sec is the initial velocity

b) let t be the time taken then

t = 124/(Vo*cos(37))

t = 124/(38.4*cos(37))

t = 4.04 sec

C) Vx = Vo*cos(37) = 38.4*cos(37) = 30.67 m/sec

Vy = Voy-(g*t) = (38.4*sin(37))-(9.8*4.04) =-16.48 m/sec

speed is V = sqrt(30.67^2+16.48^2) = 34.82 m/sec

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