Motion in a Plane

Step 1: Write the formula for range
The formula to find the range R when a body is projected is:
R=‌

u2sin‌2θ

g

Step 2: Put in the given values
Here, R=180√3m,u=60m∕s, and g=10m∕s2.
Step 3: Arrange the formula to find sin‌2θ
sin‌2θ=‌

Rg

u2

Step 4: Substitute the values
‌sin‌2θ=‌

180√3×10

60×60

‌sin‌2θ=‌

1800√3

3600

=‌

√3

2

Step 5: Identify the angle for sin‌2θ
We know that sin‌60∘=‌

√3

2

.
So, 2θ=60∘
θ=30∘
Step 6: Check for other possible angles
The range at angle θ is the same as at 90∘−θ.
So, the angle of projection can be 30∘ or 60∘.