How Does Projectile Motion Affect a Coconut's Flight from a Tree?

[PreDeadMan123]

A monkey throws a 25kg coconut from the top of a 15m high redwood with an initial velocity of 10 m/sec at an angle of 30 degrees. Find the following: A)Maximum height relative to the foot of the tree B)TIme for the entire journey C) Distance from the foot of the tree where it lands D)KE at the point of impact

 

[Hootenanny]

Again, could you please show some intial working or thoughts...

~H

 

[kyle8921]

A) To find the maximum height relative to the foot of the tree, we can use the equation for vertical motion: h = h0 + v0t + (1/2)gt^2, where h0 is the initial height (15m), v0 is the initial velocity (10 m/s), g is the acceleration due to gravity (9.8 m/s^2), and t is the time. We can rearrange this equation to solve for t and then substitute it back in to find the maximum height: t = (v0sinθ)/g, where θ is the angle (30 degrees). Plugging in the values, we get t = 1.15 seconds. Substituting this back into the equation, we get h = 15 + 10(1.15) - (1/2)(9.8)(1.15)^2 = 21.4 meters. Therefore, the maximum height relative to the foot of the tree is 21.4 meters.

B) To find the time for the entire journey, we can use the equation for horizontal motion: x = x0 + v0t + (1/2)at^2, where x0 is the initial position (0 m), v0 is the initial velocity (10 m/s), a is the acceleration (0 m/s^2), and t is the time. We can rearrange this equation to solve for t, which gives us t = x/v0. Plugging in the values, we get t = 15/(10cosθ) = 1.73 seconds. Therefore, the time for the entire journey is 1.73 seconds.

C) To find the distance from the foot of the tree where the coconut lands, we can use the same equation for horizontal motion. Plugging in the values, we get x = 0 + 10cosθ(1.73) + (1/2)(0)(1.73)^2 = 8.66 meters. Therefore, the coconut lands 8.66 meters from the foot of the tree.

D) To find the kinetic energy (KE) at the point of impact, we can use the equation KE = (1/2)mv^2, where m is the mass (25 kg) and v is the velocity. To find the velocity, we can use the Pythagorean theorem: v = √(v0