Math / Geometry

Question6 A particle is projected from rest from a point along a smooth horizontal table at $0.7 \mathrm{~m} \mathrm{~s}^{-1}$ . The table is 1 m high and stands on horizontal ground. Given that it takes 2 seconds from the moment of projection until the ball hits the ground, work out the distance from the point $A$ to the edge of the table. (4 marks)

Studdy Solution

STEP 1

Assumptions
1. The particle is projected horizontally from the edge of the table.
2. The initial horizontal velocity of the particle is $0.7 \, \text{m/s}$ .
3. The height of the table is $1 \, \text{m}$ .
4. The time taken for the particle to hit the ground is $2 \, \text{s}$ .
5. The acceleration due to gravity is $9.8 \, \text{m/s}^2$ .
6. We need to find the horizontal distance from the point of projection to the point where the particle hits the ground.

STEP 2

Calculate the horizontal distance traveled by the particle. Since there is no horizontal acceleration, the horizontal distance can be calculated using the formula:
$\text{Horizontal Distance} = \text{Initial Horizontal Velocity} \times \text{Time}$

STEP 3

Plug in the given values for the initial horizontal velocity and time:
$\text{Horizontal Distance} = 0.7 \, \text{m/s} \times 2 \, \text{s}$

STEP 4

Calculate the horizontal distance:
$\text{Horizontal Distance} = 1.4 \, \text{m}$
The distance from the point $A$ to the edge of the table is $1.4 \, \text{m}$ .

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