SEARCH HOME
 Math Central Quandaries & Queries
 Question from kwame, a student: the range R of projectile fired with an initial velocity Vo ,at an angle of elevation (@ )theta from the horizontal is given by the equation R = (Vo(squared) sin(2theta)/g. where g is the acceleration due to gravity . Find the angle theta such that the projectile has maximum range .

Kwame,

Vo and g are constants and hence R is a function of θ alone.

R(θ) = Vo2 sin(2θ)/g

Since Vo and g are constants you can differentiate R(θ) with respect to θ to get

R'(θ) = 2 Vo2 cos(2θ)/g

Solve R'(θ) = 0 for θ and then use the second derivative to verify that this value of θ yields a maximum value.

Harley

Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.