A boy throws a ball with an initial speed of 40.0 m/s. The angle of the thrown ball is 33.0° above the horizontal.(Neglect the height of the boy and air resistance.)
(a) What is the ball's speed in the horizontal direction just before it hits the ground?
(b) How long is the ball in the air?
The horizontal motion is with uniform speed vx=v0•cos33=40•0.84=33.55m/s
t=(2v0sinα)/g=2•40•0.54/9.8=4.45 s
To answer these questions, we can use the principles of projectile motion. Projectile motion refers to the motion of an object that is launched into the air and moves in a curved path under the influence of gravity.
(a) The horizontal motion and the vertical motion of the ball are independent of each other. To find the ball's speed in the horizontal direction just before it hits the ground, we only need to consider the horizontal component of its initial velocity.
We can use trigonometry to determine the horizontal component of the initial velocity. The horizontal component can be found using the equation:
Vx = V * cos(theta),
where Vx is the horizontal component of the velocity, V is the magnitude of the initial velocity, and theta is the angle above the horizontal.
In this case, V = 40.0 m/s and theta = 33.0°. Plugging these values into the equation, we can calculate:
Vx = 40.0 m/s * cos(33.0°).
Calculating this value gives us the horizontal component of the velocity.
(b) To find the time the ball is in the air, we can use the equation for the time of flight in projectile motion:
t = 2 * Vy / g,
where t is the time of flight, Vy is the vertical component of the velocity, and g is the acceleration due to gravity (approximately 9.8 m/s²).
To find Vy, we can use the equation:
Vy = V * sin(theta),
where Vy is the vertical component of the velocity, V is the magnitude of the initial velocity, and theta is the angle above the horizontal.
In this case, V = 40.0 m/s and theta = 33.0°. Plugging these values into the equation, we can calculate Vy.
Finally, we can substitute the values of Vy and g into the equation for the time of flight to find the time the ball is in the air.
Remember to use consistent units (e.g., meters and seconds) throughout the calculations.
By following these steps, you can find the answers to both parts (a) and (b) of the question.