4. (25pts) A 2022 Dodge Hellcat engine develops 707 ftlbf of torque at 4500rpm (revolutions per minute). The car weighs 5000lbf with passengers. The rear tire size is P305/35YR20. The gear ratios for the 8 speed transmission are shown: 4.71 3.14 2.11 1st gear 2nd gear 3rd gear 4th gear 5th gear 6th gear 7th gear 8th gear reverse final 1.67 1.28 1 0.84 0.67 3.32 2.62 The P305/35YR20 tire has a width of 305mm. The sidewall height is 35% of the width. The "R20" means that the tire is radial construction and the rim has a diameter of 20in. The Y means that the tire is rated for up to 186mph. Assume that the engine attaches to the transmission, transmission to final drive, final drive to wheels (rear wheel drive). If the engine is turning at 1000rpm, and if the car is in 3rd gear, the engine turns at 1000rpm. The drive shaft between the transmission and rear differential turns at 1000/2.11=473.93rpm. The wheels turn at 473.93/2.62-180.89rpm. The speed is v=r-w=15.3mph when unit conversions are done. For the rest of the problem, assume that the car is in 5th gear and the engine is turning at 4500rpm. Assume 100% efficient transfer of torque/force/power/etc. (which won't happen but this is a made-up problem). Approximate answers provided are rounded off - need your actual answers to 3 significant figures. a. Show that the wheel diameter is 28.4in and wheel radius is 14.2in. b. Find the angular velocity (in rpm) of the drive shaft and the wheels. Ans. Approximately 3500rpm and 1300rpm. C. Find the torque on the drive shaft and on the wheels. Ans. Approximately 900ftlbf and 2400ft-lbf. d. Find the speed of the car in mph (mile per hour) units. Ans. Approximately 110mph. e. Find the force of the tires to the road in lbf. Ans. Approximately 2000lbf.