Step 1: Write the formula for maximum height The formula for the highest point a projectile can reach is: H=‌
u2sin‌2θ
2g
where H is maximum height, u is the starting speed, θ is the angle of projection, and g is gravity. Step 2: Put in the given values We know H=9.8m,u=19.6ms−1, and g=9.8ms−2. We put these in the formula: 9.8=(19.6)2‌
sin‌2θ
2×9.8
Step 3: Simplify to find sin‌2θ Multiply both sides by 2×9.8 : ‌9.8=19.6×19.6×‌
sin‌2θ
2×9.8
‌⇒9.8=39.2sin‌2θ Divide both sides by 19.6, sin‌2θ=‌
1
2
Step 4: Find the angle θ sin‌θ=‌
1
√2
=sin‌45∘,so θ=45∘. Step 5: Write the formula for range R The formula for how far the projectile lands (range) is:
R=‌
u2sin‌2θ
g
Step 6: Put in the numbers Since u=19.6ms−1,θ=45∘, and g=9.8ms−2, ‌R=‌