A cannonball is launched with a speed of 170 m/s at 40 degrees above the horizontal.
Find the components into which it is resolved.
Answer (2)
The question is asking to resolve the initial velocity of a cannonball into its horizontal and vertical components. To do this, we use trigonometric functions, specifically sine and cosine, because the motion of a projectile can be analyzed using these due to the right-angle triangle that is formed by the velocity vector and its components. The initial speed of the cannonball is 170 m/s at an angle of 40 degrees above the horizontal.
To find the horizontal component (Vx), we use the cosine function: Vx = V * cos(θ) = 170 m/s * cos(40°).
To find the vertical component (Vy), we use the sine function: Vy = V * sin(θ) = 170 m/s * sin(40°).
Calculating these values:
Vx = 170 m/s * cos(40°) ≈ 130.19 m/s
Vy = 170 m/s * sin(40°) ≈ 109.44 m/s
So, the horizontal component of the cannonball's velocity is approximately 130.19 m/s, and the vertical component is approximately 109.44 m/s.
The cannonball's horizontal component of velocity is approximately 130.19 m/s, while the vertical component is approximately 109.44 m/s. This resolution utilizes trigonometric functions, namely cosine and sine, based on the launch speed and angle. Understanding these components helps analyze the projectile's motion effectively.
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