Question

Two water jets are emerging from a vessel at a height of 50 centimeters and 100 centimeters. If their horizontal velocities at the point of ejection are 1 meter/second and 0.5 meters/second respectively, calculate the ratio of their horizontal distances of impact. 1:04 1:234 2:01 1.41:1 3:02

Answer 1

For t1:

t1 = square root of 2h1 / g = square root of 2 * 0.5 / 9.8 = 0.319 sec

For t2:

t2 = sqaure root of 2h2 / g = square root of 2 * 1.0 / 9.8 = 0.451 sec

Wherein:
t = time(s) for the vertical movement
h= height
g = gravity (using the standard 9.8 m/sec measurement)

d1 = 1*0.319 = 0.319 m
d2 = 0.5 * 0.451 = 0.225 m

Where:

d = hor. distance

ratio = d1:d2
= 0.319 : 0.225
=3.19 : 2.25

The answer is 3.19 : 2.25

Answer 2

1.41 : 1

Step-by-step explanation:

time required to reach the ground is given as

`t = \sqrt{(2h)/(g)}`

now we know that

h = 50 cm and h = 100 cm

so the ratio of time of two is given as

`(t_1)/(t_2) = \sqrt{(50)/(100)}`

`(t_1)/(t_2) = \sqrt{(1)/(2)}`

now the distance traveled by the object is given as

`d = vt`

now the ratio of the distance moved is given as

`(d_1)/(d_2) = (v_1t_1)/(v_2t_2)`

`(d_1)/(d_2) = (1)/(0.5)* \sqrt{(1)/(2)}`

`(d_1)/(d_2) = \sqrt 2 = 1.41 : 1`