1. In modeling projectile motion, the distance, d(in feet) traveled by a project
ID: 3183831 • Letter: 1
Question
1. In modeling projectile motion, the distance, d(in feet) traveled by a projectile fired from the ground with an angle of elevation, 9, is related to the initial velocity, vo (in feet per second), by the equation, vo sin(20) 32d. If the projectile is pictured as being fired from the origin into the first quadrant, then the x- and y-coordinates (in feet) of the projectile at time, t (in seconds), are given by x = vot cos and y =-16t2 + vot sin . Al the local medieval games, suppose a catapult is placed 100 feet from the castle wall, which is 35 feet high. The soldier wants the burning bale of hay to clear the top of the wall and land 50 feet inside the castle wall. If the soldier estimates the initial velocity of the bale to be 70 ftsec, then at what angle should the bale of hay be launched so that it will travel 150 feet and pass over the castle wall? a) the bule of hay is launched at the angle determined in part a), how many seconds will have passed after the initial launch before the bale of hay reaches its maximum height? t what rate is the bale of hay gaining height a second after the initial launch?Explanation / Answer
From the first equation sin(2theta)=32*150/70*70
Theta=49.2°
Time taken to travel till the castle wall =100/70cos(49.2°)=2.18s
Height after 2.18s should be greater than 35ft.
Height after travelling 100 ft=-16*2.18*2.18+70*2.18*sin(49.2°)=39.47ft
its well above the castle wall
b) maximum height is reached after 70sin(49.2°)/32=1.65s
c)after initial launch bale is gaining height at the rate 52.98 ft/s
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