A girl tried to overthrow gender stereotypes by kicking her stuffed animal across a park with an initial velocity of 25m/s, making an angle of 45 degrees with the horizontal. Upon reaching maximum height, her cat jumped and propelled it further horizontally with a velocity of 15m/s.
Calculate: a) the maximum height
B) the total time of flight
C) total horizontal displacement
D) it's final velocity when it lands
the max height and time in air are the same as if the cat had left it alone.
For the horizontal displacement, figure how long it takes to fall from the max height (1/2 the total air time).
The extra displacement from the cat is the x-velocity * that time.
The final velocity on landing is the vector sum of the initial velocity (downward) + the extra 15 m/s.
To solve this problem, we can break it down into two parts: the initial projectile motion and the subsequent horizontal motion propelled by the cat.
For the initial projectile motion:
a) To find the maximum height, we need to determine the time it takes for the object to reach its peak. We know the initial velocity (25m/s) and the angle of projection (45 degrees). We can use the horizontal and vertical components of this initial velocity to solve for time.
The horizontal component of the initial velocity can be found using the formula: Vx = V * cos(θ), where V is the initial velocity and θ is the angle of projection. In this case, Vx = 25m/s * cos(45 degrees) = 17.68m/s.
The vertical component of the initial velocity can be found using the formula: Vy = V * sin(θ), where V is the initial velocity and θ is the angle of projection. In this case, Vy = 25m/s * sin(45 degrees) = 17.68m/s.
The time taken to reach the maximum height can be found using the formula: t = Vy / g, where g is the acceleration due to gravity (approximately 9.8m/s²). In this case, t = 17.68m/s / 9.8m/s² = 1.8s.
Now, let's find the maximum height using the formula: H = Vy² / (2g), where Vy is the vertical component of the initial velocity and g is the acceleration due to gravity. In this case, H = (17.68m/s)² / (2 * 9.8m/s²) = 16.04m.
Therefore, the maximum height is 16.04 meters.
b) To find the total time of flight, we need to consider both the ascent and descent of the projectile. The total time of flight is twice the time taken to reach the maximum height. Thus, the total time of flight is 2 * 1.8s = 3.6 seconds.
Moving on to the horizontal motion:
c) The total horizontal displacement can be calculated by multiplying the horizontal component of the initial velocity (Vx) by the total time of flight. In this case, total horizontal displacement = Vx * t = 17.68m/s * 3.6s = 63.65 meters.
d) Finally, to find the final velocity when the object lands (assuming no other forces act on it), we can use the formula: Vf = Vx, where Vf is the final velocity and Vx is the horizontal component of the initial velocity. In this case, Vf = 17.68m/s.
Therefore, the final velocity when the object lands is 17.68 meters per second.