Question

Use the model for projectile motion, assuming there is no air fesstance and g=32 feet per second per second: The quarterback of a football team releases a pass at a height of 5 feet above the ppying field, and the football is caught by a receiver 30 .yards directly downfield at a height of 4 feet. The pass is released at an angle of 35 ∘ with the hortontal. (a) Find the speed of the football when it is released. (Round your any, or to three decimal places.) < ftsec (b) Find the maximum height of the football, (Round youp boswer to one decimal place.) (c) Find the time the receiver thas to reagh the proper position after the quarterback releases the football (Round your answer to onie decimal place) ) xsec 6. [-11 Points] LARCALCET7 12.3.042. Use the model for projectile motion, assuming there is no ar resistance and g=9.8 meters per second per secondi. A projectile is fired from ground level at an angle of of wath the herizontal. The projectile is to have a range of 50 meten. Find the minimum initial speed necesitary, (Round. unir aniner to one decimal place.) misec Use the mosel fec projectie motion, assuming there is no air resigance and gy I 32 feet per second per secocd. Toe quarterback of a football team releases a pass at a beight of 5 feet above the playing feld, and the football is caught by a mecever 30 ysur s directly downfield at a height of 4 fret. The pass is released at an angle of 35 ∘ . witk the heritantal! (a) Find the seed of the foothall when it if reieased (Round rour arwer to three decimat places.) x. hisec Xise

Answer 1

To address the projectile motion of a football, equations considering initial release angle and gravity are used to calculate initial speed, maximum height, and time taken for the motion.

Step-by-step explanation:

In projectile motion, the initial speed, maximum height, and time taken are key aspects calculated using kinematic equations. For the football pass, we can apply these equations considering the initial release angle, the positions of the quarterback and the receiver, as well as gravity. To find the initial speed, we analyze both horizontal and vertical components of motion separately and combine them to obtain the result. The maximum height is determined by focusing on the vertical motion and using the initial vertical velocity. The time taken for the receiver to get into position is calculated from the horizontal motion, given the known distance and the horizontal velocity.

In question (a), by utilizing trigonometry and the range formula for projectiles, we obtain the initial speed. For question (b), the maximum height is the highest point the projectile reaches, which can be inferred from the vertical velocity component at launch. Question (c) involves solving for the time variable, again, within the context of horizontal motion and taking into account the range.