A worker on a roof 30 m above the ground needs to lift a 50 kg bucket of cement from the ground to a point 10m above the ground by pulling on a rope weighing 4kg/m. Write down an integral for the work required. Gravitational acceleration is 9.8 m/s².

A firework of mass 0.4 kg is fired vertically upwards with initial speed 40 m/s. The firework itself provides a force of 2 N upwards. The firework explodes after 6s. Find the height at which it explodes.

A force of 33.9 N is applied tangentially to a wheel of radius 19.9 cm and gives rise to an angular acceleration of 2.74 rad/s² Calculate the moment of inertia of the wheel. Express your answer in kg m², to at least two digits after the decimal point. plz help use g = 9.8

A ball with mass 0.05 kg is thrown upward with initial velocity 25 m/s from the roof of a building 60 m high. Assume there is a force due to |v| air resistance of magnitude directed opposite to the velocity, where 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: m b) Find the time that the ball hits the ground. Time: seconds

An object is shot straight upward from sea level with an initial velocity of 400 ft/sec. a. Assuming that gravity is the only force acting on the object, give an upper estimate for its velocity after 5 sec have elapsed. Use g = 32 ft/sec2 for the gravitational acceleration. b. Find a lower estimate for the height attained after 5 sec.

2- A constant force of (2kN) pulls a box along a level floor a distance of (10 m) in (50 s). What is the power used?

fill the tanks for two and a half hours. Calculate how many tons of fuel are in the and t is measured in hours. They tanks once they are full, rounded to the nearest ton. 2) You know the Excelsior must achieve 30,000 mph to reach escape velocity. The rocket's engines are state-of-the-art and capable of creating an acceleration based on the profile a=10t, where t is in seconds and a is in 2. Unfortunately the pull of gravity works against the'rocket's motion at 32 ,2. Neglecting wind resistance, calculate how long to burn the fuel to allow the Excelsior to achieve 30,000 mph, rounded to the nearest minute. 3) The straight-line distance from Earth Mars at the time the launch is scheduled is 100 million miles. In order to avoid other celestial bodies the Excelsior must travel in an arc given by the equation y = - (x-50)2+20, where x and y are in 125 millions of miles, and the x-axis denotes the straight-line distance to Mars. Find the actual distance travelled by the Excelsior rounded to…