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The world-renowned daredevil Anita Bath has designed a barrel in her grade 10 math class that she feels will follow a Parabolic shape down the Niagara Falls. See the picture for the trajectory that she plans on following. She believes the equation, where h is the height above the water in meters, and d is the distance from the edge of the falls in meters. There are rocks that extend 15m from the foot of the falls. Analyze the full problem and come up with a recommendation if Anita will be safe if she is able to follow the projected trajectory.

a. It is unsafe for Anita to attempt the trajectory
b. It is safe for Anita to attempt the trajectory
c. Additional information is needed to make a recommendation
d. Anita should consult a physics expert for safety advice

1 Answer

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Final answer:

Without the explicit parabolic equation or additional details about the initial conditions of Anita Bath's proposed stunt, we cannot accurately predict her trajectory and therefore cannot determine her safety. The presence of rocks 15 meters from the fall's base is a significant risk factor that must be accounted for with detailed calculations.

Step-by-step explanation:

The subject matter revolves around the physics of projectile motion, particularly analyzing the trajectory of an object (in this case, Anita Bath's barrel) descending the Niagara Falls. If Anita follows a parabolic path, theoretically described by projectile motion, it is essential to know the equation of the parabola to determine where the barrel will land relative to the dangerous rocks at the bottom. The question references a parabolic equation where h is the height above water in meters, and d is the distance from the edge of the falls in meters. However, without the explicit equation or more details about the initial conditions, such as the initial velocity, angle of launch, or the maximum height of the falls, we cannot reliably predict the barrel's trajectory.

Assuming the rocks extend 15 meters from the foot of the falls, Anita's safety will depend on whether her barrel's trajectory will clear this distance and land safely in the water beyond the rocks. If the barrel is to follow the stated parabolic shape, it would need to have sufficient horizontal displacement to avoid the rocks. While we can apply the general principles of projectile motion to grasp the potential dangers, without the specific parabolic equation or trajectory data, it is not possible to make a definitive recommendation about her safety.