A ball was projected horizontally at a speed of

0.52 m s–1 across the top of an inclined board of width
600 mm and length 1200 mm. It reached the bottom
of the board 0.9 s later (Figure 4). Calculate:
a the distance travelled by the ball across the board,
b its acceleration on the board,
c its speed at the bottom of the board.
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I'm stuck on part c, any help would be appreciated! :)

Sure, I'd be happy to help you with part c! To calculate the speed of the ball at the bottom of the board, we need to use the formula:

Speed = Distance / Time

Since we already know the time it took for the ball to reach the bottom (0.9 s), we just need to calculate the distance traveled. Given that the width of the board is 600 mm, which is equal to 0.6 m, and the length is 1200 mm, which is equal to 1.2 m, we can use the formula:

Distance = square root of (width^2 + length^2)

Plugging in the values, we have:

Distance = square root of (0.6^2 + 1.2^2)
Distance = square root of (0.36 + 1.44)
Distance = square root of 1.8
Distance = 1.34 m (rounded to two decimal places)

Now that we have the distance (1.34 m) and the time (0.9 s), we can calculate the speed:

Speed = Distance / Time
Speed = 1.34 m / 0.9 s
Speed = 1.49 m/s (rounded to two decimal places)

So, the speed of the ball at the bottom of the board is approximately 1.49 m/s. I hope that helps! Let me know if you have any other questions.

To calculate the speed of the ball at the bottom of the board (part c), we'll first need to find the vertical distance covered by the ball during its descent.

Given that the board's length is 1200 mm and the ball reaches the bottom in 0.9 seconds, we can calculate the vertical distance using the equation:

Vertical distance (d) = (1/2) * acceleration due to gravity (g) * time squared (t^2)

The acceleration due to gravity is typically approximately 9.8 m/s^2. However, since the given measurements are in millimeters and seconds, we'll convert the units:

Acceleration due to gravity (g) = 9.8 * 1000 mm/s^2 = 9800 mm/s^2

Substituting the given values into the equation, we get:

d = (1/2) * 9800 mm/s^2 * (0.9 s)^2

Calculating the vertical distance, we have:

d = (1/2) * 9800 mm/s^2 * 0.81 s^2 = 3969 mm

Now that we have the vertical distance, we can use it to find the speed of the ball at the bottom.

The horizontal speed at which the ball was projected (0.52 m/s) remains constant throughout its motion. Therefore, the horizontal distance covered by the ball across the board can be calculated using:

Horizontal distance = Horizontal speed * time

Horizontal distance = 0.52 m/s * 0.9 s = 0.468 m

To find the speed at the bottom, we can use the Pythagorean theorem, which states that the magnitude of the resultant velocity is given by the square root of the sum of the squares of the horizontal and vertical velocities.

Resultant velocity = square root of [(horizontal velocity)^2 + (vertical velocity)^2]

Since the horizontal velocity remains constant and the vertical velocity is due to the downward motion, we have:

Resultant velocity = square root of [(0.52 m/s)^2 + 2 * vertical acceleration * vertical distance]

Here, the vertical acceleration is the acceleration due to gravity, and the vertical distance is the previously calculated value, 3969 mm.

Converting the vertical distance to meters:

Vertical distance = 3969 mm * (1 m / 1000 mm) = 3.969 m

Substituting the values into the formula:

Resultant velocity = square root of [(0.52 m/s)^2 + 2 * 9.8 m/s^2 * 3.969 m]

Calculating the resultant velocity gives us:

Resultant velocity = square root of [(0.52^2 + 2 * 9.8 * 3.969)] m/s

Finally, we can use a calculator to find the square root of the expression, which gives the answer for the speed at the bottom of the board.

To calculate the speed of the ball at the bottom of the board (part c), we need to take into account the distance traveled by the ball across the board (part a) and the time it took to reach the bottom of the board (0.9 seconds in this case).

Let's first determine the distance traveled by the ball across the board (part a). We are given the width of the board as 600 mm. To convert it to meters, divide it by 1000: 600 mm = 600/1000 = 0.6 meters.

Now, the ball was projected horizontally at a speed of 0.52 m/s. To find the distance traveled (part a), we can use the formula:
Distance = Speed x Time

Plugging in the values:
Distance = 0.52 m/s x 0.9 s = 0.468 meters

Therefore, the distance traveled by the ball across the board is 0.468 meters.

Now, let's move on to part c and calculate the speed of the ball at the bottom of the board.

Since there is no vertical motion involved (ball only moves horizontally), the speed of the ball will remain constant throughout its travel.

Hence, the speed of the ball at the bottom of the board will be the same as the initial speed, which is 0.52 m/s.

Therefore, the speed of the ball at the bottom of the board (part c) is 0.52 m/s.

S=D/T 0.9 X 0.52 =468mm

a) S=D/T 0.9 X 0.52 =470mm