Final answer:
The component form of the initial velocity for a basketball shot at a 70° angle is approximately (3.42 m/s, 9.397 m/s), obtained by using cosine for the horizontal component and sine for the vertical component.
Step-by-step explanation:
To find the component form of the initial velocity of a basketball shot at a 70° angle with the horizontal and an initial velocity of 10 meters per second, we can use trigonometric functions. The horizontal component (vx) is found using the cosine function, and the vertical component (vy) is calculated using the sine function:
- vx = v0 cos(θ)
- vy = v0 sin(θ)
Where v0 is the initial speed (10 m/s) and θ is the angle of elevation (70°). Plugging in the values:
- vx = 10 m/s * cos(70°) = 10 m/s * 0.3420 = 3.42 m/s
- vy = 10 m/s * sin(70°) = 10 m/s * 0.9397 = 9.397 m/s
So the component form of the initial velocity is approximately (3.42 m/s, 9.397 m/s).