Salem throws a ball at an initial velocity of 18m/s at an angle of 53^o to the ground.
A, workout velocity in component vector
B, why will the ball spend a longer time in the air than it did before
C, calculate the range of the ball
A. vy = 18sinθ vx = 18cosθ
B. before what?
C. R = v^2/g sin2θ
on B. vy(t) = 18sinθ - 9.8t
so I guess B refers to a situation where θ < 53°
Workaut TheVelocity Incomponent Vector
A. Well, well, looks like Salem wants to play some ball! To find the velocity components, we can break down the initial velocity into horizontal and vertical components. The horizontal component (Vx) can be found using Vx = V * cos(theta), where V is the magnitude of the initial velocity (18 m/s) and theta is the launch angle (53 degrees). So, Vx = 18 m/s * cos(53°).
The vertical component (Vy) can be found using Vy = V * sin(theta), where Vy is the vertical velocity and theta is the launch angle. So, Vy = 18 m/s * sin(53°).
B. Ah, the age-old question of why things take longer to fall back to the ground. Well, my friend, it's all about that vertical component. When Salem throws the ball at an angle, the vertical component not only helps the ball to go up but also slows down its descent. So, the ball will end up spending more time in the air compared to throwing it straight up.
C. Now it's time to calculate the range of the ball. The range is the horizontal distance the ball travels before hitting the ground. To find it, we need to know the time of flight (T) of the ball, which is the total time it spends in the air.
To calculate T, we use the formula T = (2 * Vy) / g, where g is the acceleration due to gravity (approximately 9.8 m/s^2). Once we have T, we can find the range (R) using the formula R = Vx * T.
So, let's plug in the values:
Vx = 18 m/s * cos(53°)
Vy = 18 m/s * sin(53°)
T = (2 * Vy) / g
R = Vx * T
I'll let you do the math! Remember, though, practice makes perfect, especially if you're practicing throwing balls like Salem!
A. To determine the velocity in component vector form, we need to break down the initial velocity into horizontal and vertical components.
The horizontal component (Vx) can be found using the formula: Vx = V * cos(θ), where V is the magnitude of the initial velocity (18 m/s) and θ is the launch angle (53°).
Vx = 18 m/s * cos(53°) = 10.85 m/s (rounded to two decimal places)
The vertical component (Vy) can be found using the formula: Vy = V * sin(θ).
Vy = 18 m/s * sin(53°) = 14.12 m/s (rounded to two decimal places)
Therefore, the velocity in component vector form is (10.85 m/s, 14.12 m/s).
B. The ball will spend a longer time in the air than before because the vertical component of the initial velocity contributes to the time of flight. As gravity acts on the ball, it decelerates the vertical component of the velocity until it reaches its maximum height. From there, gravity continues to accelerate the ball downwards, increasing the time it spends in the air.
C. To calculate the range of the ball, we need to determine the horizontal distance it travels. The formula to calculate the range (R) is: R = (V^2 * sin(2θ)) / g, where V is the initial velocity (18 m/s), θ is the launch angle (53°), and g is the acceleration due to gravity (9.8 m/s^2).
R = (18 m/s)^2 * sin(2 * 53°) / (9.8 m/s^2) ≈ 34.92 meters (rounded to two decimal places)
Therefore, the range of the ball is approximately 34.92 meters.