A ball that is hit or thrown horizontally ball that is hit or thrown horizontally with a velocity of v metres per second will travel a distance d metres before hitting the ground, where d=v square root h/ 4.9 and h is the height, in metres, from which the ball is hit or thrown.
a) Use the properties of radicals to rewrite the formula with a rational denominator. (2 marks)
b) How far will a ball that is hit with a velocity of 45 m/s at a height of 0.8 m above the ground travel before hitting the ground, to the nearest tenth of a metre? (2 marks)
apparently the formula is
d = v√(h/4.9)
multiply that by √4.9/√4.9 and you have
d = v√(4.9h)/4.9
Now just plug in the numbers.
a) To rewrite the formula with a rational denominator, we need to eliminate the square root in the formula.
We start with the given formula: d = v √(h/4.9).
To eliminate the square root, we can multiply the numerator and denominator of the fraction by the square root of the denominator.
So, the formula with a rational denominator is: d = v * ( √h / √(4.9) ) * ( √(4.9) / √(4.9) ).
Simplifying the expression further, we get: d = ( v * √(4.9h) ) / 4.9.
b) Using the formula d = ( v * √(4.9h) ) / 4.9, we can substitute the given values: v = 45 m/s and h = 0.8 m.
Therefore, d = ( 45 * √(4.9 * 0.8) ) / 4.9.
Simplifying this expression, we have: d = ( 45 * √(3.92) ) / 4.9.
Calculating the square root of 3.92, we get approximately 1.98.
Substituting this value in the formula, we get: d ≈ ( 45 * 1.98 ) / 4.9.
Simplifying further, we have: d ≈ 89.1 / 4.9.
Calculating this division, we find: d ≈ 18.2.
Therefore, the ball will travel approximately 18.2 meters before hitting the ground to the nearest tenth of a meter.
a) To rewrite the formula with a rational denominator, we need to eliminate the square root from the denominator. One way to achieve this is by multiplying both the numerator and denominator by the conjugate of the denominator, which will eliminate the square root.
The conjugate of √h is √h. Multiplying the numerator and denominator by the conjugate, we get:
d = v * √h / 4.9 * √h
Simplifying this expression, we have:
d = v√h / 4.9√h
Since the square root of h in the numerator and denominator cancels out, we can rewrite the formula with a rational denominator as:
d = v / 4.9
b) We are asked to find the distance traveled by a ball hit with a velocity of 45 m/s at a height of 0.8 m above the ground.
Plugging the given values into the formula, we have:
d = 45 / 4.9
Calculating this, we get:
d ≈ 9.1837
Therefore, the ball will travel approximately 9.2 meters before hitting the ground, to the nearest tenth of a meter.