Step 1: Write the formula for maximum height
The formula for the highest point a projectile can reach is:
H=‌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)2‌Step 3: Simplify to find
sin‌2θMultiply both sides by
2×9.8 :
‌9.8=19.6×19.6×‌‌⇒9.8=39.2sin‌2θDivide both sides by 19.6,
sin‌2θ=‌Step 4: Find the angle
θsin‌θ=‌=sin‌45∘,soθ=45∘.Step 5: Write the formula for range
RThe formula for how far the projectile lands (range) is:
R=‌Step 6: Put in the numbers
Since
u=19.6ms−1,θ=45∘, and
g=9.8ms−2,
‌R=‌| (19.6)2×sin‌(2×45∘) |
| 9.8 |
‌sin‌(90∘)=1,‌ so ‌‌R=‌‌R=‌=39.2m
