Pebble accelerated by the wind with a starting velocity

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The discussion focuses on calculating the velocity and angle of a pebble accelerated by wind using differential equations and the quadratic formula. The initial displacement equation was identified as incorrect due to the factor of 6.0. The calculations for horizontal and vertical velocities yielded results of 11.6 m/s and 7.7 m/s, respectively, leading to a resultant velocity of 13.9 m/s. The angle of projection was determined to be 33.4 degrees using vector components. The conversation emphasizes the importance of using standard kinematics equations for accurate results.
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Homework Statement
A moderate wind accelerates a pebble over a horizontal xy plane with a constant acceleration ##\vec a = (6.0i + 7.0j)m/s^2##. At time t = 0, the velocity is ##(5.0i)m/s## . What are the (a) magnitude and (b) angle of its velocity when it has been displaced by 13.0 m parallel to the x axis?
Relevant Equations
$$x = \frac {-b \pm \sqrt{b^2 -4ac}} {2a}$$
$$V=\sqrt {V_x^2 + V_y^2} $$
$$a_x=a \cos\Theta$$
I first used differentials to find an equation for the displacement.
$$6.0t^2+5.0t=13$$
and using the quadratic formula I got time ##t=1.1##
I then got ##V_x## from ##6.0t+5.0=v_x=11.6##
and ##V_y## from ##7.0t=v_y=7.7##
The I got v from ##V=\sqrt {V_x^2 + Vy^2} ##
$$\sqrt {11.6^2 + 7.7^2} =13.9 m/s$$

Which I took as my velocity.

from there I used the vector vector competent equation ##a_x=a \cos\Theta## to find the angle

##\cos^{-1}\frac {11.6} {13.9}=\Theta=33.4##
 
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Ursa said:
I first used differentials to find an equation for the displacement.
$$6.0t^2+5.0t=13$$
The factor of 6.0 in the first term is not correct. Check the standard kinematics equations for displacement with constant acceleration. Otherwise, your method of solution looks good.
 
There is no need to find the time.
There are five standard SUVAT equations, each involving four of time, displacement, acceleration, initial velocity, final velocity.
Which three of those are you given, and which are you trying to find? Which SUVAT equation uses just those four?
 
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