find the modulus of the resultant of the velocities 10ms-1 and 8ms-1 inclined at an angle of 60 degree

z^2 = 10^2 + 8^2 - 2*10*8 cos120°

Find the modulus of the resultant of the velocities 8m5 and 6m5 inclined at an angle of 60

Oh, I see you're looking for the modulus of the resultant velocities. How about we take a little detour from all those equations and calculations and have some fun? Let's "mod-ulus" our way into a funny scenario to find an answer!

Imagine the velocities 10 m/s and 8 m/s are two friends named Speedy and Swift. They decide to go on a thrilling adventure in a crazy amusement park. Speedy, being faster, takes the lead, but Swift is determined to keep up.

Now, they come across a giant inclined ramp with an angle of 60 degrees. Speedy takes off, zooming up the incline with his 10 m/s velocity while Swift follows closely behind with his 8 m/s velocity. As they reach the top of the ramp, something incredible happens...

They collide in mid-air, resulting in a hilarious somersault circus act, spinning and twirling through the sky! It's like a clown performance you'd see at a circus – utterly fantastic!

Now, as they land safely back on the ground, we suddenly realize, we got a bit carried away with the comedy routine and forgot to calculate the modulus of the resultant velocities. Oops!

But fret not! To find the modulus of the resultant velocities, we can use some math "magic." We'll use the Pythagorean theorem, which states that in a right triangle, like the one formed here, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

So, let's use this theorem to get back on track. The square of the hypotenuse (resultant) will be the sum of the squares of Speedy's and Swift's velocities. By calculating the square root of this sum, we'll finally have the modulus of their resultant velocities.

Modulus of Resultant Velocities = √(10^2 + 8^2)

And voila! Just calculate the square of both numbers, add them up, take the square root of the sum, and you'll have your answer. Remember, laughter is the best medicine, even when it comes to math!

To find the modulus of the resultant velocity, we can use the concept of vector addition.

Step 1: Break down the given velocities into their horizontal and vertical components.

The horizontal component for a velocity of 10 m/s inclined at an angle of 60 degrees is calculated as:
10 m/s * cos(60 degrees) = 10 * 0.5 = 5 m/s

The vertical component for a velocity of 10 m/s inclined at an angle of 60 degrees is calculated as:
10 m/s * sin(60 degrees) = 10 * √3/2 = 5√3 m/s

Similarly, for the velocity of 8 m/s inclined at an angle of 60 degrees:
Horizontal component = 8 m/s * cos(60 degrees) = 8 * 0.5 = 4 m/s
Vertical component = 8 m/s * sin(60 degrees) = 8 * √3/2 = 4√3 m/s

Step 2: Add the horizontal and vertical components separately for both velocities.

Horizontal component of the resultant velocity = 5 m/s + 4 m/s = 9 m/s
Vertical component of the resultant velocity = 5√3 m/s + 4√3 m/s = 9√3 m/s

Step 3: Use the Pythagorean theorem to find the modulus (magnitude) of the resultant velocity.

Modulus of the resultant velocity (V) = √((horizontal component)^2 + (vertical component)^2)
V = √(9^2 + (9√3)^2)
V = √(81 + 243)
V = √324
V = 18 m/s

Therefore, the modulus of the resultant velocity of the given velocities is 18 m/s.

To find the modulus of the resultant velocity, you can use vector addition. The modulus (or magnitude) of a vector can be calculated using the Pythagorean theorem.

Given:
Velocity 1 = 10 m/s
Velocity 2 = 8 m/s
Angle between the velocities = 60 degrees

To find the resultant velocity, follow these steps:

Step 1: Convert the velocities into their horizontal and vertical components.
Velocity 1 = 10 m/s at an angle of 0 degrees
- Horizontal component: 10 m/s * cos(0) = 10 m/s
- Vertical component: 10 m/s * sin(0) = 0 m/s

Velocity 2 = 8 m/s at an angle of 60 degrees
- Horizontal component: 8 m/s * cos(60) = 4 m/s
- Vertical component: 8 m/s * sin(60) = 6.928 m/s

Step 2: Add the horizontal components and the vertical components separately.
Horizontal component = 10 m/s + 4 m/s = 14 m/s
Vertical component = 0 m/s + 6.928 m/s = 6.928 m/s

Step 3: Use the Pythagorean theorem to find the magnitude of the resultant velocity.
Resultant velocity (modulus) = sqrt((Horizontal component)^2 + (Vertical component)^2)
Resultant velocity = sqrt((14 m/s)^2 + (6.928 m/s)^2)
Resultant velocity ≈ sqrt(196 + 48) m/s
Resultant velocity ≈ sqrt(244) m/s
Resultant velocity ≈ 15.62 m/s (rounded to two decimal places)

So, the modulus of the resultant velocity is approximately 15.62 m/s.