A projectile has a range of 100 m when the angle of projection is 20°. Calculate the initial velocity of the projectile.

Sure, to solve this problem, we will use the formula for the range of a projectile, which is given by:

R = (v² sin 2θ) / g

where: R is the range, v is the initial velocity, θ is the angle of projection, and g is the acceleration due to gravity.

We are given: R = 100 m, θ = 20°, and g = 9.8 m/s².

We need to find v.

First, we need to convert the angle from degrees to radians because the trigonometric functions in the formula use radians.

1 radian = 180/π degrees So, 20° = 20 * π/180 = 0.349 radians.

Next, we substitute the given values into the formula and solve for v:

100 = (v² sin 20.349) / 9.8 100 * 9.8 = v² * sin(20.349) 980 = v² * sin(0.698) 980 / sin(0.698) = v² v² = 980 / sin(0.698) v = sqrt(980 / sin(0.698))

Now, calculate the value of v using a calculator to get the initial velocity of the projectile.