calculus
posted by andrew .
1. Consider a projectile, say a frictionless teddy bear, which is thrown at an angle of theta with an initial
velocity of v0.
a) For a fi xed angle, and the maximum height of the teddy bear.
b) Calculate the distance that the teddy bear travels before returning (gently, of course) to the
ground (which is assumed to be
at).
c) Use these pieces of information to nd the angle which produces the maximum of the sum of height and distance.
usage of function. in these question.

calculus 
Damon
Vi = Vo sin T
u = Vo cos T
v = Vi  gt
max height when v = 0
0 = Vosin T  g t
t = Vo sin T / g
h = 0 + Vi t  .5 g t^2
max h = Vo sin T [Vo sin T/g]  .5 g[Vo sin T / g]^2
max h = [.5 /g][VosinT]^2
(this is quicker to get using potential and kinetic energy argumenents. Note max height of course when T = 90 degrees, straight up)
Now part b
the total time in the air is twice the time needed to reach max altitude so
total t = 2 Vo sin T/g
d = u t = Vo t cos T
d = Vo [ 2 Vo sinT/g]cos T
d = [2 Vo^2/g] sin T cos T
part c
Sum = S = [.5 /g][VosinT]^2 + [2 Vo^2/g] sin T cos T
dS/dT = 0 at max
0= [.5Vo^2/g]sin Tcos T+[2Vo^2/g][sin^2T+cos^2T]
0=2 cos^2T .5 sin T cosT 2 sin^2T
but 2 (cos^2Tsin^2T)=2 cos2T
0= 2 cos 2T .5 sinTcosT
but sinTcosT =.5 sin2T
so
0=2 cos2T .25 sin2T
sin2T/cos2T = 8 = tan 2T
2T = 82.8 degrees
T = 41.4 degrees
Interesting, max range is at 45 degrees. I may have made an arithmetic error in that mess. 
calculus 
andrew
@Damon : Appreciate it sir. u are a life saver. i was on track and needed a kick . thanks alot.
Respond to this Question
Similar Questions

Physics/Calculus
At a county fair, a boy and two friends bring their teddy bears on the giant Ferris wheel. The wheel has a diameter of 14.8 m, the bottom of the wheel is 1.8 m above the ground and its rim is moving at a speed of 1.0 m/s. The boys … 
Physics
At a county fair, a boy takes his teddy bear on the giant Ferris wheel. Unfortunately, at the top of the ride, he accidentally drops his stuffed buddy. The wheel has a diameter of 14.6 m, the bottom of the wheel is 1.1 m above the … 
munir
1. Consider a projectile, say a frictionless teddy bear, which is thrown at an angle of theta with an initial velocity of v0. a) For a fi xed angle, and the maximum height of the teddy bear. b) Calculate the distance that the … 
Physics
At a county fair, a boy takes his teddy bear on the giant Ferris wheel. Unfortunately, at the top of the ride, he accidentally drops his stuffed buddy. The wheel has a diameter of 14.6 m, the bottom of the wheel is 2.4 m above the … 
Physics
At a county fair, a boy and two friends bring their teddy bears on the giant Ferris wheel. The wheel has a diameter of 14.3 m, the bottom of the wheel is 1.9 m above the ground and its rim is moving at a speed of 1.0 m/s. The boys … 
Kinder math
Cover the teddy bears in the top row with different color teddy bear counters. Color the teddy bears in the bottom row to show the colors. 
math
My son is in Kindergarten and I have no idea about the "Counters" in the question: 1st) Cover the teddy bears in the top row with differentcolor teddy bear counters. 2nd) Color the teddy bears in the bottom row to show the colors." … 
Science
At a county fair, a boy takes his teddy bear on the giant Ferris wheel. Unfortunately, at the top of the ride, he accidentally drops his stuffed buddy. The wheel has a diameter of 15.3 m, the bottom of the wheel is 3.37 m above the … 
social studies
Baby Lilithâ€™s big sister has taken Lilithâ€™s new teddy bear from her and has hidden it in the closet. Baby Lilith will look for the teddy bear if she has developed: object permanence. visual preference. crossmodal transfer. causality. … 
English
1. Sam is looking for his teddy bear. 2. Sam is looking for his toy bear. (Are both OK?