Question

Derive the formula for Range of a projectile (R).​

Answer 1

Answer:

The range (R) of the projectile is the horizontal distance it travels during the motion. Using this equation vertically, we have that a = -g (the acceleration due to gravity) and the initial velocity in the vertical direction is usina (by resolving). Hence: y = utsina - ½ gt2 (1)

Answer 2

Range

The range (R) of the projectile is the horizontal distance it travels during the motion.

Now, s = ut + ½ at2

Using this equation vertically, we have that a = -g (the acceleration due to gravity) and the initial velocity in the vertical direction is usina (by resolving). Hence:

y = utsina - ½ gt2 (1)

Using the equation horizontally:

x = utcosa (2)

Remember, there is no acceleration horizontally so a = 0 here.

When the particle returns to the ground, y = 0. Substituting this into (1):

0 = utsina - ½ gt2

t (usina - ½ gt) = 0

t = 0 or t = 2u sina (3)

g

Therefore when x = R, t = 2u sina / g

Substituting into (2):

R = ucosa (2u sina)

g

The range is therefore

u²sin2alpha/g