Posted: November 2nd, 2015

Calculus

Calculus

Solve the problem. Unless stated otherwise, assume that the projectile flight is

ideal, that the launch angle is measuredfrom the horizontal, and that the

projectile is launched from the origin over a horizontal surface

1) An ideal projectile is launched from the origin at an angle of a radians to the

horizontal
and an initial speed of 175 ft./sec. Find the position function  r(t) for this

projectile.

2) A baseball is hit when it is 3.3 ft. above the ground. It leaves the bat with

an initial velocity
of 126 ft./sec at a launch angle of 30Æ. At the instant the ball is hit, an

instantaneous gust of
wind blows against the ball, adding a component of -10.5 i (ft/sec) to the ball’s

initial
velocity. How high does the baseball go? Round your answer to the nearest tenth.

Provide an appropriate response.

3) A golf ball leaves the ground at a 26Æ angle at a speed of 89 ft/sec. Will it

clear the top of a
30 ft. tree that is in the way, 133 ft. down the fairway? Explain.

4) Convert (-1,1, 6) from rectangular to spherical.

5) Convert (1,-1,4) from rectangular ot cylindrical.

6) A WWII Battleship is floating in Lake Guntersville at a point with coordinates:

Latitude
34 degrees 36 minutes 3.84 N seconds. Longitude 86 degrees 59.7 seconds W. The

ships
elevation is 601 ft. above sea level.Section High School’s football stadium has a

latitude of 34
degrees 35 minutes and .46seconds N Longitude 85 degrees 58 minutes 57.71 seconds

W. The
stadium sits 1324 ft. above sea level.

This class of battleship used a 16″/45 caliber Mar 6 Gun. Find the launch angle

required
for this battleship to drop a High capacity shell into the stadium.

What about an armor piercing shell?

What if the wind is blowing towards the battleship at 20 MPH?

What if the wind is blowing away from the battleship at 20 MPH?

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