Certainly! Let's analyze the situation.
In projectile motion, an object is influenced by the force of gravity. Gravity plays a crucial role in determining the motion of the object, particularly in the vertical (y) direction. The standard acceleration due to gravity on the surface of the Earth is approximately [tex]\( -9.8 \, m/s^2 \)[/tex]. This negative sign indicates that gravity acts downward.
Given this understanding, let's evaluate the options provided for [tex]\( a_y \)[/tex]:
1. [tex]\( -9.8 \, m/s^2 \)[/tex]
2. [tex]\( 0 \, m/s^2 \)[/tex]
3. [tex]\( \frac{1}{2} \, m/s^2 \)[/tex]
4. [tex]\( 1.0 \, m/s^2 \)[/tex]
In projectile motion, the only vertical acceleration acting on the object is due to gravity, which we know is [tex]\( -9.8 \, m/s^2 \)[/tex]. All the other values provided do not represent the acceleration due to gravity and are therefore incorrect.
Thus, for the vertical acceleration [tex]\( a_y \)[/tex] in the context of projectile motion, the correct value is:
[tex]\[ a_y = -9.8 \, m/s^2 \][/tex]
Therefore, the correct answer is:
[tex]\[ -9.8 \, m/s^2 \][/tex]
Hence, in the formula [tex]\( v_y = a_y \Delta t \)[/tex], the value of [tex]\( a_y \)[/tex] for an object in projectile motion is:
[tex]\[ -9.8 \, m/s^2 \][/tex]
