A rock is thrown at an upward angle of 40° to the horizontal with a speed of 20 m/s. (a) What is its initial horizontal velocity? (b) What is its horizontal velocity 1.0 s after launch?
=(cos(40))(20)
=(0.76)(20)
=15.32m/s
Horizontal velocity doesn't change, so the answer a and b would be the same.
To solve this problem, we can use the given information to determine the initial and final horizontal velocities of the rock.
(a) To find the initial horizontal velocity, we can use the basic trigonometric relationship between the angle and the horizontal and vertical components of the velocity. The horizontal component of the velocity is given by v₀x = v₀ cosθ, where v₀ is the initial velocity and θ is the angle of launch.
So, the initial horizontal velocity (v₀x) = 20 m/s * cos(40°).
(b) To find the horizontal velocity 1.0 second after launch, we need to determine the change in the horizontal velocity over that time. Since there are no horizontal forces acting on the rock (ignoring air resistance), the horizontal velocity remains constant.
Therefore, the horizontal velocity 1.0 second after launch will be the same as the initial horizontal velocity.
Now let's calculate the values:
(a) The initial horizontal velocity (v₀x) = 20 m/s * cos(40°)
v₀x = 20 m/s * 0.766 = 15.32 m/s
(b) The horizontal velocity 1.0 second after launch will be the same as the initial horizontal velocity.
Therefore, the horizontal velocity 1.0 s after launch is also 15.32 m/s.
So, the answers to the questions are:
(a) The initial horizontal velocity is 15.32 m/s.
(b) The horizontal velocity 1.0 s after launch is 15.32 m/s.
To solve this problem, we can use the formulas of projectile motion. Let's break down the given information and solve for each part:
(a) What is the initial horizontal velocity?
The initial horizontal velocity refers to the velocity in the horizontal direction before any external forces act on the object. In this case, the rock is thrown at an upward angle of 40° to the horizontal with a speed of 20 m/s. To find the initial horizontal velocity, we need to find the horizontal component of the velocity.
We can use the equation:
horizontal velocity = initial velocity × cos(angle)
Given that the initial velocity is 20 m/s and the angle is 40°, we can calculate the horizontal velocity as:
horizontal velocity = 20 m/s × cos(40°)
Using a scientific calculator, the result is approximately 15.32 m/s.
So, the initial horizontal velocity of the rock is approximately 15.32 m/s.
(b) What is the horizontal velocity 1.0 s after launch?
To find the horizontal velocity 1.0 s after launch, we need to consider that there is no horizontal acceleration. So, the horizontal velocity remains constant throughout the motion.
Therefore, the horizontal velocity 1.0 s after launch will be the same as the initial horizontal velocity, which is approximately 15.32 m/s.
So, the horizontal velocity 1.0 s after launch is approximately 15.32 m/s.