Question

You throw a ball at an angle of 30° above the horizontal at a wall 20 m away. the ball’s initial speed is 15 m>s, and it leaves your hand at a height of 1.5 m above the ground.

(a) how long does the ball take to get to the wall?

Answer 1

The problem is solved by finding the horizontal velocity component of the initial speed and then using it to calculate the time it takes for the ball to reach a wall 20 m away. The calculation shows that it takes approximately 1.54 seconds for the ball to reach the wall.

Step-by-step explanation:

The given problem involves calculating the time a ball takes to travel horizontally to a wall at a distance of 20 m when thrown with an initial speed of 15 m/s at an angle of 30°. To solve this, we need to separate the initial velocity (15 m/s) into its horizontal (Vx) and vertical (Vy) components using trigonometry.

The horizontal velocity component can be found using “Vx = V cos(30°)”, where V is the initial speed. The time taken to reach the wall would then be calculated using the horizontal distance and the horizontal velocity component by “t = distance / Vx”.

Let's calculate the horizontal velocity component:

Vx = 15 m/s × cos(30°)

Vx = 15 m/s × (√3/2)

Vx ≈ 15 m/s × 0.866

Vx ≈ 12.99 m/s (rounded to two decimal places)

Now, we can find the time to reach the wall:

t = distance / Vx

t = 20 m / 12.99 m/s

t ≈ 1.54 seconds (rounded to two decimal places)

The ball takes approximately 1.54 seconds to reach the wall.