1- Find the velocity i and the position x as functions ôf mass m, which starts from rest at x =0 and t=0, subject to the followin functions: (a) F = F.+ ct (b) Fx = F, sin ct c) F, = F, e Where F, and c are positive constants.
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- The velocity vector of the boat has two components: v1 is the velocity of the water, and v2 is the velocity of the boat relative to the water. If v1=3mi/h and v2=5mi/h, determine the velocity vector of the boat.A particle moves in a circle with a diameter of 120 cm. If its linear velocity is given by v = 4.5t where v is in mps and t is in s, find the radial, tangential and the resultant acceleration of the particle.In the feasibility test, the flight movement of a drone is known to have a position function height h (t) = t2 - t - 2, where t is in minutes and height h is in meters. Determine the average speed of the drone increments at intervals of 3 minutes to 6 minutes and then determine the instantaneous velocity exactly equal to the average velocity.
- A motorboat and its load weigh 2150 N. Assume that the propeller force is constant and equal to 110N, and the water resistance is numerically equal to 6.7V, where V is the speed at any instant time in m/sec. If the boat starts from rest, determine its distance at the end of 10 seconds.A motorboat and its load weigh 2150 N. Assume that the propeller force is constant and equal to 110N, and the water resistance is numerically equal to 6.7V, where V is the speed at any instant time in m/sec. If the boat starts from rest, determine its speed at the end of 10 seconds.Q1. A driver enters a curved car at 72 km/h, slows down, causing the speed to drop at a steady rate of 4.5 km/h every second. If the radius of curvature is 16.7 m. Find the acceleration of the car after 4 seconds from the driver starting to slow down.
- Specifically a dynamics problem: Two rockets start from rest at the same elevation. Rocket A accelerates vertically at 20 m/s2 for 12 s and then maintains a constant speed. Rocket B accelerates at 15 m/s2 until reaching a constant speed of 150 m/s.Construct the a-t, v-t, and s-t graphs for each rocket until t = 20 s. What is the distance between both rockets when t = 20 s?A 5-ton spacecraft is running low on fuel and the spacecraft's propulsion force is given by F=5000−2x (The instant the force reaches zero, the fuel runs out and the force is forever zero.) Assuming that the change in the ship's mass due to fuel loss is negligible, determine: a) Graph the force versus position and tell where the fuel ends. b) How much energy was available in the fuel? c) If the ship starts from rest, what is the fastest speed the ship can reach?A boat is towed at the rate of 12mi/hr. At t = 0, the towing line is cast off and a man in the boat begins to row in the direction of motion exerting force of 20 lb. The combined weight of the man and the boat is 480lb. The water resists the motion with a force equal to 1.7v lb, where v is the velocity of the boat in feet per second. Derive a DE leading the velocity of the boat.
- TOPIC: Equation of Motion (NORMAL AND TANGENTIAL) Fn= Man Ft= Mat Given a 1400 kg car that travels along a road with increasing vertical profile y = 0.0003x². If the constant velocity of the car is 30 m/s. of the distance is at 210m, Determine the x-component of the velocity (m/s) of the car. Compute the total force (KN). PLEASE ANSWER WITH A COMPLETE AND DETAILED SOLUTIONS. THANK YOUNEED COMPLETE SOLUTION AND ANSWER ASAP. A golf ball is launched with the initial conditions shown in the figure. Determine the radius of curvature of the trajectory and the time rate of change of the speed of the ball (a) just after launch and (b) at apex. Neglect aerodynamic drag. (b) At the apex, determine the speed v of the ball, the total acceleration a of the ball, the normal component of acceleration an and the tangential component of acceleration at.Answers: v = ft/sec a = ft/sec2 an = ft/sec2 at = ft/sec2an automobile starting from rest speeds up to 12 m/s with a constant acceleration of 1.2 m/s^2. runs at fast speed for some time, and finally comes to rest with a decelaration of 1.5 m/s^2. if the total distance travelled is 319m, find the total time required. draw the v-t and s-t curves.