Explanations & Calculations
- Gravitational acceleration ≈9.8ms−2≈32.17ms−2
a)
- Apply suitable formula out of the 4 for both horizontal and vertical motions of the projectile.
↑−257.6fttt=(193.2sin30)fts−1×t+21×(−32.17fts−2)×t2=8.0or−2.0=8.0s
- Then the horizontal coverage would be
→s=ut=193.2.cos30fts−1×8.0s=1338.5ft
b)
- Apply s=ut+1/2at2 downwards for the travel for that time.
↓d=0+21×(+9.8ms−2)×(0.2s)2≈0.2m
- Apply the same formula for the dart's horizontal motion.
→=10ms−1×0.2s=2m
c)
- Apply the standard formula for the horizontal range of a projectile for this case.
R4575msin2θθ∵sin2θθ∴θ=gv2.sin2θ=9.8ms−2(366ms−1)2.sin2θ=0.33=9.60=cos(90−2θ)=90−9.6=80.40=9.60or80.40
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