When a 80kg block of mass is pushed by 400 Newton at an angle of 37 degrees above the horizontal to accelerate from 20 m/s what will be the final velocity after 6 second

Is it pushed up or down the slope?

Is that 20 m/s up slope or down slope?
I will assume both are UP and you will have to get it straight yourself.

weight component down slope = m g sin 37
= 80 * 9.81 * sin 37 = 472 N

If you are pushing up with 400 N, you lose, at least on earth.

a = (400-472)/80 = - 0.9 m/s^2

if it started with 20 m/s UP
V = Vi -0.9 t
V = 20 - 0.9 (6)
V = 14.6 m/s

If my assumption of directions is wrong, you fix it.

I assume that the block of mass m=80 kg slides horizontally, and that the force F=400N pushes downwards at an angle of θ=37° below the horizontal.

Initial horizontal velocity is u=20 m/s, and we look for velocity v at time t=6 seconds.

Further assumption: friction μ=0.

Horizontal component of applied force
= Fcos(θ)
acceleration,
a=F/m=400cos(θ)/80=5cos(θ)

use kinematics equation
v=u+at
=20 m/s + 5cos(37) m/s^2 * 6
=20+23.959 m/s
=43.959 m/s

Ah, did not think of that :)

To calculate the final velocity of the block after 6 seconds, we need to use the equation of motion that relates force, mass, acceleration, and time.

Here are the steps to calculate the final velocity:

Step 1: Write down the given information:
Mass (m) = 80 kg
Force (F) = 400 Newtons
Angle (θ) = 37 degrees
Initial velocity (u) = 20 m/s
Time (t) = 6 seconds

Step 2: Resolve the force into its vertical and horizontal components:
Vertical component of force = F * sin(θ)
Horizontal component of force = F * cos(θ)

Let's calculate these values:

Vertical component of force:
F_vertical = 400 Newtons * sin(37 degrees)
F_vertical = 240 Newtons

Horizontal component of force:
F_horizontal = 400 Newtons * cos(37 degrees)
F_horizontal = 320 Newtons

Step 3: Calculate the acceleration using Newton's second law of motion:
F_horizontal = mass * acceleration
acceleration = F_horizontal / mass

acceleration = 320 Newtons / 80 kg = 4 m/s²

Step 4: Use the equation of motion to calculate the final velocity:
v = u + (a * t)

where:
v = final velocity
u = initial velocity
a = acceleration
t = time

Plugging in the values:

v = 20 m/s + (4 m/s² * 6 seconds)
v = 20 m/s + 24 m/s
v = 44 m/s

Therefore, the final velocity of the block after 6 seconds will be 44 m/s.