# Projectile motion variation of range

#### mpm166

For a launched projectile, what are the following theoretical relationships/proportionalities:
• variation of range with speed of projectile, keeping a constant launch angle
• variation of range with launching angle, keeping the launching speed constant

thanks for the help

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#### arildno

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In order to solve these questions, you should assume in addition:
a) that the ground is flat
b) That the projectile has initial vertical position at ground level
c) That no other forces than gravity acts upon the projectile
d) That the acceleration of gravity, g, is constant
In general, you will then have parameters determining the range:
1. g
2. Launch angle, $$\theta_{0}$$
3. Initial speed, $$V_{0}$$

That is, range R can be regarded as a function $$R=R(g,V_{0},\theta_{0})$$.

Solution procedure:
1.Solving the vertical component of the equation of motion will give you the time at which the projectile lands.
2. Plug that time value into the horizontal position function, and you have the range R

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