Question

Problem:

Ash throws a Pokéball at an upwards angle of 30° above the horizontal with a speed of 5m/s
trying to catch a shiny Castform. If the Castform is on the ground and hit, find how far away it
was, as well as the max height the ball reaches. Assume the acceleration of the gravity for the
planet they are on has a value of g=9.8m/s^2 and we can ignore air resistance.
Draw a well labeled diagram of the physical situation. Make sure the initial velocity is drawn as
a vector and the trajectory is drawn, showing the coordinate axes with directions. Label
accelerations and the point where the ball reaches max height.
Hints: break the initial velocity into x and y parts, solve the y parts of the problem to find the
time, then use the result to solve the y parts.

Answer 1

Step-by-step explanation:

Here is a step by step explanation of how to solve the problem:

Break the initial velocity into x and y components. The velocity of the Pokéball can be broken down into two components: the horizontal component (vix) and the vertical component (viy). The horizontal component remains constant throughout the motion and has a value of vix = vcosθ, where v is the magnitude of the velocity and θ is the angle of launch. The vertical component changes due to the acceleration of gravity and has a value of viy = vsinθ - gt, where t is time.

Solve for the time of flight. We want to find the time it takes for the Pokéball to reach its maximum height, so we need to set viy = 0 and solve for t:

0 = vsinθ - gt

gt = vsinθ

t = vsinθ / g

Calculate the maximum height. The maximum height is reached when the vertical component of velocity is equal to zero, so we can use the equation:

h = viy^2 / (2g)

h = (vsinθ)^2 / (2g)

Calculate the range. The range is the horizontal distance traveled by the Pokéball during its flight, and it can be found using the equation:

x = vix * t

x = vcosθ * (vsinθ / g)

Draw a well labeled diagram of the physical situation. Draw the coordinate axes, showing the directions, and label the initial velocity as a vector. Show the trajectory of the Pokéball, including the point where it reaches its maximum height, and label the acceleration due to gravity.