6. A skydiver of mass m = 60 kg leaps from a plane with an initial upward velocity of vo = +5 m/s. Assume the diver experiences air resistance proportional and opposite to their velocity, with drag coefficient b= 11 N/(m/s). Also assume acceleration due to gravity is g = 9.8 m/s². The velocity of the diver changes with time, as modelled by the following differential equation. m =-mg-bv du dt Solve for v(t)= the velocity of the diver at time t, and determine the diver's terminal velocity: lim v(t)
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- You place a crate of mass 40.9 kg on a frictionless 2.64-meter-long incline. You release the crate from rest, and it begins to slide down, eventually reaching the bottom 1.52 s after you released it. What is the angle of the incline? 17.6 degrees 13.5 degrees 21.6 degrees 25.9 degreesYou place a crate of mass 43.2 kg on a frictionless 4.99-meter-long incline. You release the crate from rest, and it begins to slide down, eventually reaching the bottom 1.99 s after you released it. What is the angle of the incline? 17.9 degrees 14.9 degrees 20.9 degrees 25.1 degreesYou place a crate of mass 20.3 kg on a frictionless 2.61-meter-long incline. You release the crate from rest, and it begins to slide down, eventually reaching the bottom 1.01 s after you released it. What is the angle of the incline? 37.7 degrees 31.4 degrees 44.0 degrees 57.2 degrees
- You place a crate of mass 36.4 kg on a frictionless 3.71-meter-long incline. You release the crate from rest, and it begins to slide down, eventually reaching the bottom 1.56 s after you released it. What is the angle of the incline? 40.8 degrees 22.7 degrees 18.1 degrees 27.2 degrees5. A student throws a 0.1 kg ball into the air. (A) Just after the ball leaves their hand, it has a velocity of 5 m/s. (B) At the peak of its motion, it has a velocity of 2 m/s. Assuming no air resistance, to what height dịd the student throw the ball? Also, assume the ball started at h=0 (The zero-reference line is at the starting position of the ball). The energy chart is optional. KE- Vz- Poson A SystemFlow Poston KE- 1.2SJ@ A KE /2..1.2 KE- 0.25 @B Etr E, E Ea Et E, E En Energy Equation KETGPE = KE + GPE 6. A parachutist of mass 50.0 kg jumps out of a stationary balloon at a height of 1,000 meters. The system consists of the parachutist and the Earth, if the parachutist lands with a speed of 5.0 m/s, how much energy was transferred out of the system (so energy transferred to something else)? 7. Suppose the spring below has a spring constant of 50. N/m. The box has a mass of 8.0 kg and rests on a surface of negligible friction. In the diagram above, the spring was compressed 4.0 m.…You place a crate of mass 26.3 kg on a frictionless 4.29-meter-long incline. You release the crate from rest, and it begins to slide down, eventually reaching the bottom 1.66 s after you released it. What is the angle of the incline? 18.5 degrees 22.2 degrees 26.6 degrees 20.4 degrees
- A ball is thrown upward from the ground with velocity vi= 14 m/s and reaches height of h above the ground before falling back down. Take the upward direction to be positive. Refer to the figure. Neglect Air resistance. The acceleration in m/s to the ball when it is in the air is -9.8 m/s. The velocity of the ball in meters sped second, when it reaches the top of its trajectory is 0 m/s. Enter an expression for the maximum height, h, the ball reached in terms of vf, vi, and a. The value of h in meters is 10 m. Enter an expression for the time it takes for the ball to travel from the ground to the top, delta t, in terms of vi, vf, and a. The value of delta t in seconds is 10s. The total displacement in meters, of the ball going through its entire motion: reveling from the ground to the tio and then falling back to the ground is 0m. Enter an expression for the total time of flight of the ball: the time from when it is launched to when it lands back in the ground. Express this in terms of…You place a crate of mass 31.6 kg on a frictionless 3.00-meter-long incline. You release the crate from rest, and it begins to slide down, eventually reaching the bottom 1.34 s after you released it. What is the angle of the incline? A 24.9 degrees B 19.9 degrees C 29.9 degrees D 44.9 degreesA car travels west at 30 miles an hour for 10 min West. The car then makes a u turn and travels east 45 miles per hour for fifteen min east. What is the cars total displacement? A- 10km W B-10 km E C- 26 km E D - 26 km W E- 6.2 km W
- ycla 3. A car travelling at 122 km/h strikes a tree, the front end of the car compresses, and the driver comes to rest after traveling 0.558 m. What was the average acceleration of the driver during the collision? Express your answer in terms of g's (1.00g = 9.80 m/s'). g's %3D Given the fact that humans can withstand a maximum of 25 g's for a short time without brainy injury, what would the condition of this driver most likely be? Impact khl l1. A golf ball is hit from ground level with initial velocity given x(t)= 3 m/s(t) in a direction that is due east and at an angle theta above the horizontal. Neglecting air resistance, use Newton's second law to find the position as a function of time, using coordinates with x measured east and y north. Find the time for the golf ball to return to the ground and how far it travels in that time.At what altitude above the Earth's surface is the acceleration due to gravity equal to g/ 2? h = ? m