A ball with mass 0.75 kg is thrown upward with initial velocity 25 m/s from the roof of a building 20 m high. Assume there is a force due to air resistance of magnitude directed opposite to the velocity, where |v| 30 the velocity v is measured in m/s. NOTE: Use g=9.8 m/s² as the acceleration due to gravity. Round your answers to 2 decimal places. a) Find the maximum height above the ground that the ball reaches. Height: 51.89 m Time: 5.81 X b) Find the time that the ball hits the ground. seconds X c) Use a graphing utility to plot the graphs of velocity and position versus time.

The analytical method of adding vectors expressed in terms of their components may be applied to vectors in three dimensions, for which graphical work is inconvenient. Find the magnitude of the resultant of the vectors A = il2 - j37 + k58 and B = i5 + j30 - k42, where i, j, and k are unit vectors along the x, y, and z axes, respectively.

1d.  A student stands at the edge of a cliff and throws a stone horizontally over the edge with a speed of  v0 = 18.5 m/s. The cliff is h = 20.0 m above a flat, horizontal beach as shown in the figure. Write the equations for the position of the stone with time, using the coordinates in the figure. (Use the following as necessary: t. Let the variable t be measured in seconds. Do not state units in your answer.) x=  y=

A cheetah leaps horizontally from a 5-meter high rock at a speed of 3.5 m/s. How far from the base of the rock will the cheetah land?If the cheetah leaps at an angle of 17 degress Celsius, how much farther will it land?

A space shuttle lands on a distant planet where the gravitational acceleration is 2.0 ( We do not know thelocal units of length and time , but they are consistent throughout the problem). The shuttle coasts along aleve, frictionless plane with a speed of 6.0. It then coasts up a frictionless ramp of height 5.0 and angle 0f 30°.After a brief ballistic flight, it lands a distance S from the ramp. Solve for S in local units of length. Assume theshuttle is small compared to the local length unit and that all atmospheric effects are negligible. Use x and y  components.

A guided missile is propelled from the origin of a coordinate system with the x-axis along the ground and the y-axis vertical. Its path, or trajectory, is given by the equation  y = 464x − 16x2.  Find the object's maximum height.  Answer in units

The acceleration of a particle is a constant. At t=0 the velocity of the particle is (14.91 + 18.4ĵ) m/s. At t = 4.6 s the velocity is 11.4j m/s. (Use the following as necessary: t. Do not include units in your answers.) (a) What is the particle's acceleration (in m/s²)? = î+ 18.4 v(t) = (b) How do the position (in m) and velocity (in m/s) vary with time? Assume the particle is initially at the origin. r(t) = î+ X Î- i) m/s m/s

A velocity vector has a magnitude of 1.85 m/s and makes an angle of 155 ̊ with the +x axis.(a) Sketch a diagram of the vector and show the x and y components.(b) Calculate the x and y components of the vector.

Problem 4: Vector Addition. Vector A = 200 NZ45° counterclockwise from the z axis, and vector B = 300 N 270° counterclockwise from the y axis. Find the resultant R= A + B by addition of scalar components. Problem 5: Consider the picture below. Find the tension T, tension Ta tension T₂

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