# Projectile Motion

ProjectileMotion

Question

Aslingshot is launched 60 feet from a 30 feet high firewall. It isrequired that the burning cotton roll is displaced from the peak tofall into a pool of water positioned 40 feet into the firewall. Thecotton roll commences at 75 feet per second initial velocity.Determine the launching angle for the cotton roll such that it passeson top of the firewall and cover 100 feet total distance.

Solution

Accordingto Gibson (2008),

Equation(1)

Initialvelocity, =75feet per second.

Totaldistance covered, *d*=100 feet

Substitutingin equation (1):

SinceSin 2θ is positive, the angle falls either in the first or secondquadrant. Therefore,

Inthe first quadrant when2θ=34.7°, θ=17.35°

Inthe second quadrant when2θ= (180°-34.7°), θ=72.65°

Forthe burning roll to attain at least 40 feet high at the point itcrosses the firewall after covering 60 feet,Gibson (2008), states that the horizontal distance covered is givenby:

Equation(2)

For:

Similarly,according to Gibson(2008), thevertical distance covered is determined using equation (3) below.

Equation(3)

=7.502 feet

Theheight is below the 40 feet mark hence 17.35°isnot the appropriate angle.

For:

Substitutingfor t in equation (3) above gives:

=76.94 feet

Theheight exceeds the minimum value of 40 feet when projected at 72.65°.Therefore, this is the recommended launching angle for the cottonroll.

References

Gibson, J.(2008). *Projectile motion*. Los Angeles, LA: TMW Media Group.

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