How to update the value of child component's props from parent component?

From my parent component, I need to trigger a child component's portion of code containing a Firebase query. Note that in the child component, that code is triggered within the mounted() hook (but in order to execute it from the parent component, I suppose I will have to move that code to a method or something).

What is the recommended way to achieve such a thing?

Here's my parent component code - simplified for clarity:

<template>
  <div>
    <nav>
      <v-btn @click="viewNextWeek"></v-btn>
    </nav>
    <project-row :mon="mon"></new-row-form>
  </div>
</template>

<script>
import ProjectRow from './ProjectRow.vue';
import store from '../store';
import moment from 'moment';

export default {
  name: 'home',
  components: {
    ProjectRow
  },
  data() {
    return {
      mon: moment().startOf('isoWeek')
    }
  },
  methods: {
    viewNextWeek: function() {
      this.mon = moment().startOf('isoWeek').add(7, 'days');
    }
  }
}
</script>

Child component - simplified too:

<template>
  <div>
    <input v-model="monTime">
  </div>
</template>

<script>
import { db } from '../firebase';

export default {
  props: [
    'mon'
  ],
  mounted() {
    var timesRef = db.collection('times');
    var timesWeek = timesRef.where('date', '==', this.mon);
    timesWeek.get()
    .then((querySnapshot) => {      
      querySnapshot.forEach((doc) => {
        this.monTime = doc.data().time;
      });
    })
    .catch(function(error) {
      console.log('Error getting documents: ', error);
    });  
  }
}
</script>